What must you add to an even integer to get the next greater even integer?

Odds and even numbers alternate, meaning that if you start from an odd number, the next will be even, then odd, then even, then odd ...

So, if you count skipping twos, you will always meet odd numbers if you start from an odd number, or even numbers if you start from an even number.

For example, if we start from 4 (even), and count skipping twos, we'll count

4, 6, 8, 10, 12, 14, 16, ...

which are all even.

Similarly, if we start from 15 (odd) and count skipping twos, we'll count

15, 17, 19, 21, 23, 25, ...

which are all odd.

So, the answer is 2. If you add 2 to an even number, you'll skip the odd number immediately after it, and land on the next even number.