As far as correctness goes, this only works for Unicode Code Points in the Basic Multilingual Plane (those that can be represented by a single two byte char in Java). If you have characters outside of that, you will get two chars with an individual surrogate pair in each of them to represent a single real world character.

I use a for loop to iterate the string and use charAt() to get each character to examine it. Since the String is implemented with an array, the charAt() method is a constant time operation.

String s = "...stuff...";

for (int i = 0; i < s.length(); i++){
    char c = s.charAt(i);        
    //Process char
}

That's what I would do. It seems the easiest to me.

Zero-based index

You are getting the error because the value of i is going beyond the last index available in Hello. The last index in Hello is "Hello".length() - 1 whereas the value of i is going beyond this value because of your loop terminating condition:

i < string.length() *  num;

By the way, if you want to repeat Hello 3 times, you should do it as

for(int i = 0; i < num; i ++){
   System.out.print(string);
}

Demo:

public class Main {
    public static void main(String[] args) {
        final String string = "Hello";
        final int num = 3;
        for (int i = 0; i < num; i++) {
            System.out.print(string);
        }
    }
}

String#repeat

With Java 11+, you can do it without using a loop by using String#repeat:

System.out.println(string.repeat(num));

Demo:

public class Main {
    public static void main(String[] args) {
        final String string = "Hello";
        final int num = 3;
        System.out.println(string.repeat(num));
    }
}