This is such a bad question lol. Part of it relies on you just knowing how leap years work.

There is a mistake in the description of the problem:

"either or" is XOR, not OR. You do have to use OR though.

I severely don't understand why my output is always ~ no response on stdout ~ when I put the actual tests into custom input input: 25-06-2365 07-09-8847 output: ~ no response on stdout ~

There's no code for JavaScript

Java:

here is the sol:

import java.util.; import java.lang.; import java.io.; import java.math.;

public class Main {

public static int month[];

public static void main (String[] args) throws java.lang.Exception {
    Scanner in  = new Scanner(System.in);

    month = new int[15];

    String s = in.nextLine();

    StringTokenizer str = new StringTokenizer(s, "- ");

    int d1 = Integer.parseInt(str.nextToken());
    int m1 = Integer.parseInt(str.nextToken());
    int y1 = Integer.parseInt(str.nextToken());
    int d2 = Integer.parseInt(str.nextToken());
    int m2 = Integer.parseInt(str.nextToken());
    int y2 = Integer.parseInt(str.nextToken());

    int result = findPrimeDates(d1, m1, y1, d2, m2, y2);
    System.out.println(result);

}

public static void updateLeapYear(int year) {
    if(year % 400 == 0) {
        month[2] = 29;     //correction 1
    } else if(year % 100 == 0) {
        month[2] = 28;    //correction 2
    } else if(year % 4 == 0) {
        month[2] = 29;
    } else {
        month[2] = 28;
    }
}

public static void storeMonth() {
    month[1] = 31;
    month[2] = 28;
    month[3] = 31;
    month[4] = 30;
    month[5] = 31;
    month[6] = 30;
    month[7] = 31;
    month[8] = 31;
    month[9] = 30;
    month[10] = 31;
    month[11] = 30;
    month[12] = 31;
}

public static int findPrimeDates(int d1, int m1, int y1, int d2, int m2, int y2) { storeMonth();

    int result = 0;

    while(true) {
        int x = d1;
        x = x * 100 + m1;
        x = x * 10000 + y1;    //correction 3
        if(x % 4 == 0 || x % 7 == 0) {    //correction 4
            result = result + 1;
        }
        if(d1 == d2 && m1 == m2 && y1 == y2) {
            break;
        }
        updateLeapYear(y1);
        d1 = d1 + 1;
        if(d1 > month[m1]) {
            m1 = m1 + 1;
            d1 = 1;
            if(m1 > 12) {
                y1 =  y1 + 1;
                m1 = 1;         //correction 5
            }
        }
    }
    return result;
}

}