Java Program

import java.util.Scanner;

public class CartonPacking {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N;
        System.out.print("Enter number of boxes: ");
        N = sc.nextInt();

        // Check for invalid input
        if (N <= 0 || N > 1000) {
            System.out.println("INVALID INPUT");
            return;
        }

        int totalBoxes = N;
        int c48 = 0, c24 = 0, c12 = 0, c6 = 0;

        // 48 capacity cartons
        c48 = N / 48;
        N = N % 48;

        // 24 capacity cartons
        c24 = N / 24;
        N = N % 24;

        // 12 capacity cartons
        c12 = N / 12;
        N = N % 12;

        // 6 capacity cartons
        c6 = N / 6;
        N = N % 6;

        // If boxes left less than 6, use one extra carton of 6
        if (N > 0) {
            c6 = c6 + 1;
        }

        int totalCartons = c48 + c24 + c12 + c6;

        // Display break-up
        if (c48 > 0)
            System.out.println("48 * " + c48 + " = " + (48 * c48));

        if (c24 > 0)
            System.out.println("24 * " + c24 + " = " + (24 * c24));

        if (c12 > 0)
            System.out.println("12 * " + c12 + " = " + (12 * c12));

        if (c6 > 0)
            System.out.println("6 * " + c6 + " = " + (6 * c6));

        System.out.println("Remaining boxes = 0");
        System.out.println("Total number of boxes = " + totalBoxes);
        System.out.println("Total number of cartons = " + totalCartons);

        sc.close();
    }
}

Sample Run

Enter number of boxes: 726

48 * 15 = 720
6 * 1 = 6
Remaining boxes = 0
Total number of boxes = 726
Total number of cartons = 16