I want to generate 6 different random numbers by using Math.random and store them into an array. How can I make sure that they are different? I know I need to use for-loop to check the array but how...

This is the range. I only need numbers between 1 and 49. ( 1 + (int) (Math.random() * 49) )

In Java 8:

final int[] ints = new Random().ints(1, 50).distinct().limit(6).toArray();

In Java 7:

public static void main(final String[] args) throws Exception {
    final Random random = new Random();
    final Set<Integer> intSet = new HashSet<>();
    while (intSet.size() < 6) {
        intSet.add(random.nextInt(49) + 1);
    }
    final int[] ints = new int[intSet.size()];
    final Iterator<Integer> iter = intSet.iterator();
    for (int i = 0; iter.hasNext(); ++i) {
        ints[i] = iter.next();
    }
    System.out.println(Arrays.toString(ints));
}

Just a little messier. Not helped by the fact that it's pretty tedious to unbox the Set<Integer> into an int[].

It should be noted that this solution should be fine of the number of required values is significantly smaller than the range. As 1..49 is quite a lot larger than 6 you're fine. Otherwise performance rapidly degrades.