Accessing an element inside an Array of an Array

preferredArr[0].getFirstName(), work because the object is in preferredArr. to be exact the reference of the object.
arr[0][0].getFirstName(): also, work, because also, only the reference to the same object is stored in arr[0][0].

class Customer {
    protected String firstName;
    protected String lastName;
    protected String ID;
    protected float  amountSpent;

    // Contructor
    Customer(String firstName, String lastName, String ID, float  amountSpent)
    {
        this.firstName = firstName;
        this.lastName = lastName;
        this.ID = ID;
        this.amountSpent = amountSpent;
    }
    
    // Accessors and mutators
    
    public String getFirstName()
    {
        return this.firstName;
    }
}

class Gold extends Customer {
    protected int discount;

    // overloaded contructor
    Gold(String firstName, String lastName, String ID, int discount, float  amountSpent)
    {
        super(firstName, lastName, ID, amountSpent);
        this.discount = discount;
    }
    // Accessors and mutator
}

public class Main
{
    public static void main(String[] args) 
    {
        
        Customer[][] arr = new Customer[2][1];

        Customer[] preferredArr = new Gold[3];
        Customer[] regularArr = new Customer[3];
        
        preferredArr[0] = new Gold("John", "Doe", "1234", 45, 0.12f);
        regularArr[0] = new Customer("Caroline", "Merritt", "5678", 60);
        
        arr[0] = preferredArr;
        arr[1] = regularArr;
        
        System.out.println("preferredArr[0].getFirstName() = "+preferredArr[0].getFirstName());
        
        System.out.println("arr[0][0].getFirstName() = "+arr[0][0].getFirstName());   

    }
}

The result :

preferredArr[0].getFirstName() = John                                                           
arr[0][0].getFirstName() = John

You can check this : two references to the same object.
And where the object in java are stored
Good Luck.