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Try this:

int state = 0; 
int led;
int ledState;

void loop() {  
  while (Serial.available())
  {
    if (state == 0)
    {
      led = Serial.read() - '0';
      if(led >= 0 && led <= 7)
      {
        state = 1; // Here we have got the LED number, go to state 1
        continue; 
      }
    }
    if (state == 1)
    {
        ledState = Serial.read() - '0';
        if(ledState == 0)
        {
          shiftWrite(led,LOW);
        }
        else if(ledState == 1)
        {
          shiftWrite(led,HIGH); 
        }
        state = 0; // Here we ended the operation, return back to state 0
    }
  }    
        
}

You need what we call a state machine, here I use state=0 for the state corresponding to choosing LED number, state=1 is for the state that waits for the operation ON/OFF.

You're assuming that the microcontroller is going to wait until you choose LED state, which is wrong. Try this:

int state = 0; 
int led;
int ledState;

void loop() {  
  while (Serial.available())
  {
    if (state == 0)
    {
      led = Serial.read() - '0';
      if(led >= 0 && led <= 7)
      {
        state = 1; // Here we have got the LED number, go to state 1
        continue; 
      }
    }
    if (state == 1)
    {
        ledState = Serial.read() - '0';
        if(ledState == 0)
        {
          shiftWrite(led,LOW);
        }
        else if(ledState == 1)
        {
          shiftWrite(led,HIGH); 
        }
        state = 0; // Here we ended the operation, return back to state 0
    }
  }    
        
}

You need what we call a state machine, here I use state=0 for the state corresponding to choosing LED number, state=1 is for the state that waits for the operation ON/OFF.

Try this:

int state = 0; 
int led;
int ledState;

void loop() {  
  while (Serial.available())
  {
    if (state == 0)
    {
      led = Serial.read() - '0';
      if(led >= 0 && led <= 7)
      {
        state = 1;
        continue;
      }
    }
    if (state == 1)
    {
        ledState = Serial.read() - '0';
        if(ledState == 0)
        {
          shiftWrite(led,LOW);
        }
        else if(ledState == 1)
        {
          shiftWrite(led,HIGH); 
        }
        state = 0;
    }
  }    
        
}

You need what we call a state machine, here I use state=0 for the state corresponding to choosing LED number, state=1 is for the state that waits for the operation ON/OFF.

Try this:

int state = 0; 
int led;
int ledState;

void loop() {  
  while (Serial.available())
  {
    if (state == 0)
    {
      led = Serial.read() - '0';
      if(led >= 0 && led <= 7)
      {
        state = 1; // Here we have got the LED number, go to state 1
        continue; 
      }
    }
    if (state == 1)
    {
        ledState = Serial.read() - '0';
        if(ledState == 0)
        {
          shiftWrite(led,LOW);
        }
        else if(ledState == 1)
        {
          shiftWrite(led,HIGH); 
        }
        state = 0; // Here we ended the operation, return back to state 0
    }
  }    
        
}

You need what we call a state machine, here I use state=0 for the state corresponding to choosing LED number, state=1 is for the state that waits for the operation ON/OFF.

Try this:

int state = 0;
int led;
int ledState;

void loop() {  
  while (Serial.available())
  {
    if (state == 0)
    {
      led = Serial.read() - '0';
      if(led >= 0 && led <= 7)
      {
        state = 1;
        continue;
      }
    }
    if (state == 1)
    {
        ledState = Serial.read() - '0';
        if(ledState == 0)
        {
          shiftWrite(led,LOW);
        }
        else if(ledState == 1)
        {
          shiftWrite(led,HIGH); 
        }
        state = 0;
    }
  }    
        
}

Try this:

int state = 0; 
int led;
int ledState;

void loop() {  
  while (Serial.available())
  {
    if (state == 0)
    {
      led = Serial.read() - '0';
      if(led >= 0 && led <= 7)
      {
        state = 1;
        continue;
      }
    }
    if (state == 1)
    {
        ledState = Serial.read() - '0';
        if(ledState == 0)
        {
          shiftWrite(led,LOW);
        }
        else if(ledState == 1)
        {
          shiftWrite(led,HIGH); 
        }
        state = 0;
    }
  }    
        
}

You need what we call a state machine, here I use state=0 for the state corresponding to choosing LED number, state=1 is for the state that waits for the operation ON/OFF.