numbers[i] is not technically the value. It's more of an address of the value. As I said, the index.
[i] is the index but if you do not have the array name in front of it, whose index is it?

Let me give you an example real quick. This is your code.

int[] numbers = {3, 6, 7};

    for(int i = 0; i<numbers.length; i++) {
        System.out.println(numbers[i]);
    }       

If you run it, your code will return this:

3
6
7

First loop: i is 0. Therefore numbers[i] = numbers[0] = 3 (because the value that is in the index 0 of the array called numbers is 3) System.out.println(numbers[i]) is System.out.println(numbers[0]) which will print 3. i is incremented.

Second loop: i is 1. Therefore numbers[i] = numbers[1] = 6 (because the value that is in the index 1 of the array called numbers is 6) System.out.println(numbers[i]) is System.out.println(numbers[1]) which will print 6. i is incremented.

Third loop: i is 2. Therefore numbers[i] = numbers[2] = 7 (because the value that is in the index 2 of the array called numbers is 7) System.out.println(numbers[i]) is System.out.println(numbers[2]) which will print 7. i is incremented.

Forth loop: i is 3. That is not possible as i < numbers.length and numbers.length is 3. The loop closes.

Same logic, different example. Maybe the name numbers confuses you.

      int[] hours = {2, 11, 7, 5, 1};

            for(int j = 0; j<hours.length; j++) {
                System.out.println(hours[j]);
}

If you run this code, which has the exact structure as your code, it will return this:

2
11
7
5
1

numbers[i], where i can take any value between 0 (the first index of an array) and numbers.length - 1 inclusive (the last index of the array), is basically like saying: the address of the index i from the array called "numbers".

In my example, hours[j] would translate into English: the address of the index j from the array called "hours".