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#include <Bounce2.h>

byte led1State = LOW;
byte timer1Active = 0;
const byte led1Pin = LED_BUILTIN;
const byte buttonPin1 = 6;
const byte buttonPin2 = 7;
unsigned int timer1Counter = 0;
const unsigned long debouncerInterval = 50;
const unsigned long oneSecond = 1000;
unsigned long previousMillis = 0;

Bounce debouncer = Bounce();
Bounce debouncer2 = Bounce();

void setup(){
  Serial.begin(9600);
  debouncer.attach(buttonPin1, INPUT_PULLUP);
  debouncer.interval(debouncerInterval);
  debouncer2.attach(buttonPin2, INPUT_PULLUP);
  debouncer2.interval(debouncerInterval);
  pinMode(led1Pin, OUTPUT);
}

void loop(){

  unsigned long currentMillis = millis();

  // 4 hour, 30 second timer.
  if((currentMillis - previousMillis >= oneSecond) && (timer1Active == 1)){
    previousMillis = currentMillis;
    timer1Counter++;
    if(timer1Counter < 31){
      if(led1State == LOW){
        led1State = HIGH;
      }
      else{
        led1State = LOW;
      }
      digitalWrite(led1Pin, led1State);
    }
    else if(timer1Counter == 31){
      digitalWrite(led1Pin, LOW);
    }

    // 60 sec X 60 min X 4 hours + 30 seconds.
    if(timer1Counter > 14430){
      timer1Counter = 0;
    }
  }

  // Button 1
  if(debouncer.update()){
    if(debouncer.read() == 0){
      Serial.println("Start 30 second ON, 4 hour OFF timer.");
      timer1Active = 1;
      timer1Counter = 0;
    }
  }

  // Button 2
  if(debouncer2.update()){
    if(debouncer2.read() == 0){
      Serial.println("Start 1 minute ON, 4 hour OFF timer.");
      timer1Active = 0;
      digitalWrite(led1Pin, LOW);
    }
  }

}

#include <Bounce2.h>

byte led1State = LOW;
byte timer1Active = 0;
const byte led1Pin = LED_BUILTIN;
const byte buttonPin1 = 6;
const byte buttonPin2 = 7;
unsigned int timer1Counter = 0;
const unsigned long debouncerInterval = 50;
const unsigned long oneSecond = 1000;
unsigned long previousMillis = 0;

Bounce debouncer = Bounce();
Bounce debouncer2 = Bounce();

void setup(){
  Serial.begin(9600);
  debouncer.attach(buttonPin1, INPUT_PULLUP);
  debouncer.interval(debouncerInterval);
  debouncer2.attach(buttonPin2, INPUT_PULLUP);
  debouncer2.interval(debouncerInterval);
  pinMode(led1Pin, OUTPUT);
}

void loop(){

  unsigned long currentMillis = millis();

  // 4 hour, 30 second timer.
  if((currentMillis - previousMillis >= oneSecond) && (timer1Active == 1)){
    previousMillis = currentMillis;
    timer1Counter++;
    if(timer1Counter < 31){
      //if(led1State == LOW){
        led1State = HIGH;
      //}
      //else{
        //led1State = LOW;
      //}
      digitalWrite(led1Pin, led1State);
    }
    else if(timer1Counter == 31){
      digitalWrite(led1Pin, LOW);
    }

    // 60 sec X 60 min X 4 hours + 30 seconds.
    if(timer1Counter > 14430){
      timer1Counter = 0;
    }
  }

  // Button 1
  if(debouncer.update()){
    if(debouncer.read() == 0){
      Serial.println("Start 30 second ON, 4 hour OFF timer.");
      timer1Active = 1;
      timer1Counter = 0;
    }
  }

  // Button 2
  if(debouncer2.update()){
    if(debouncer2.read() == 0){
      Serial.println("Start 1 minute ON, 4 hour OFF timer.");
      timer1Active = 0;
      digitalWrite(led1Pin, LOW);
    }
  }

}

Based on this part of your last comment "I’ve a trick! ‘const unsigned long oneSecond = 1000;’ should be edited to ‘const unsigned long oneSecond = 10;’ this make the led be as a constant ON.", it sounds like you want the LED to remain ON constantly for the 30 or 60 seconds. I have "commented out" 5 lines of the above sketch that will make this happen.

#include <Bounce2.h>

const byte buttonPin1 = 6;
const byte buttonPin2 = 7;
const unsigned long debouncerInterval = 50;

Bounce debouncer = Bounce();
Bounce debouncer2 = Bounce();

void setup(){
  Serial.begin(9600);
  debouncer.attach(buttonPin1, INPUT_PULLUP);
  debouncer.interval(debouncerInterval);
  debouncer2.attach(buttonPin2, INPUT_PULLUP);
  debouncer2.interval(debouncerInterval);
}

void loop(){

  // Button 1
  if(debouncer.update()){
    if(debouncer.read() == 0){
      Serial.println("Start 30 second ON, 4 hour OFF timer.");
    }
  }

  // Button 2
  if(debouncer2.update()){
    if(debouncer2.read() == 0){
      Serial.println("Start 1 minute ON, 4 hour OFF timer.");
    }
  }

}

EDIT

To make an LED flash on and off, and to keep time, you can use the millis() function. I started with the BlinkWithoutDelay tutorial, and came up with the following sketch. It only has one timer / LED flasher, but there is enough information in the sketch to figure out how to make the second timer / LED flasher.

#include <Bounce2.h> 

byte led1State = LOW;
byte timer1Active = 0;
const byte led1Pin = LED_BUILTIN;
const byte buttonPin1 = 6;
const byte buttonPin2 = 7;
unsigned int timer1Counter = 0;
const unsigned long debouncerInterval = 50;
const unsigned long oneSecond = 1000;
unsigned long previousMillis = 0;

Bounce debouncer = Bounce();
Bounce debouncer2 = Bounce();

void setup(){
  Serial.begin(9600);
  debouncer.attach(buttonPin1, INPUT_PULLUP);
  debouncer.interval(debouncerInterval);
  debouncer2.attach(buttonPin2, INPUT_PULLUP);
  debouncer2.interval(debouncerInterval);
  pinMode(led1Pin, OUTPUT);
}

void loop(){

  unsigned long currentMillis = millis();

  // 4 hour, 30 second timer.
  if((currentMillis - previousMillis >= oneSecond) && (timer1Active == 1)){
    previousMillis = currentMillis;
    timer1Counter++;
    if(timer1Counter < 31){
      if(led1State == LOW){
        led1State = HIGH;
      }
      else{
        led1State = LOW;
      }
      digitalWrite(led1Pin, led1State);
    }
    else if(timer1Counter == 31){
      digitalWrite(led1Pin, LOW);
    }

    // 60 sec X 60 min X 4 hours + 30 seconds.
    if(timer1Counter > 14430){
      timer1Counter = 0;
    }
  }

  // Button 1
  if(debouncer.update()){
    if(debouncer.read() == 0){
      Serial.println("Start 30 second ON, 4 hour OFF timer.");
      timer1Active = 1;
      timer1Counter = 0;
    }
  }

  // Button 2
  if(debouncer2.update()){
    if(debouncer2.read() == 0){
      Serial.println("Start 1 minute ON, 4 hour OFF timer.");
      timer1Active = 0;
      digitalWrite(led1Pin, LOW);
    }
  }

}

In response to your comment on Matej's answer @Ibrahim.M: "I wish I can abbreviate it with only one UNO that able to do the same task by using programming.". You can do this with just one Uno.

I would start by detecting the button presses and debouncing them. This is easy to do using the Bounce2 library. You can use the button presses to start timers which will turn the LEDs On and Off.

#include <Bounce2.h>

const byte buttonPin1 = 6;
const byte buttonPin2 = 7;
const unsigned long debouncerInterval = 50;

Bounce debouncer = Bounce();
Bounce debouncer2 = Bounce();

void setup(){
  Serial.begin(9600);
  debouncer.attach(buttonPin1, INPUT_PULLUP);
  debouncer.interval(debouncerInterval);
  debouncer2.attach(buttonPin2, INPUT_PULLUP);
  debouncer2.interval(debouncerInterval);
}

void loop(){

  // Button 1
  if(debouncer.update()){
    if(debouncer.read() == 0){
      Serial.println("Start 30 second ON, 4 hour OFF timer.");
    }
  }

  // Button 2
  if(debouncer2.update()){
    if(debouncer2.read() == 0){
      Serial.println("Start 1 minute ON, 4 hour OFF timer.");
    }
  }

}

EDIT

Based on the comments so far, let's agree on what each button does. The following statements are TRUE about button S1:

1. Pressing this button starts a LED flashing on pin D12, and stops the LED flashing on D11 (IF it was flashing).

2. The LED on D12 will flash on/off for 1 minute then turn off for 4 hours. After the 4 hours, the LED will remain Off.

3. The flash rate of this LED is 500ms On, 500ms Off.

The following statements are TRUE about button S2:

1. Pressing this button starts a LED flashing on pin D11, and stops the LED flashing on D12 (IF it was flashing).

2. The LED on D11 will flash on/off for 30 seconds then turn off for 4 hours. After the 4 hours, the LED will remain Off.

3. The flash rate of this LED is 500ms On, 500ms Off.

Please leave a comment to let me know if this is what you are trying to achieve. Are there any errors or omissions in the "button" specifications?

In response to your comment on Matej's answer @Ibrahim.M: "I wish I can abbreviate it with only one UNO that able to do the same task by using programming.". You can do this with just one Uno.

I would start by detecting the button presses and debouncing them. This is easy to do using the Bounce2 library. You can use the button presses to start timers which will turn the LEDs On and Off.

#include <Bounce2.h>

const byte buttonPin1 = 6;
const byte buttonPin2 = 7;
const unsigned long debouncerInterval = 50;

Bounce debouncer = Bounce();
Bounce debouncer2 = Bounce();

void setup(){
  Serial.begin(9600);
  debouncer.attach(buttonPin1, INPUT_PULLUP);
  debouncer.interval(debouncerInterval);
  debouncer2.attach(buttonPin2, INPUT_PULLUP);
  debouncer2.interval(debouncerInterval);
}

void loop(){

  // Button 1
  if(debouncer.update()){
    if(debouncer.read() == 0){
      Serial.println("Start 30 second ON, 4 hour OFF timer.");
    }
  }

  // Button 2
  if(debouncer2.update()){
    if(debouncer2.read() == 0){
      Serial.println("Start 1 minute ON, 4 hour OFF timer.");
    }
  }

}