6, 9, 12, 15 which pair of numbers has an odd product and an even sum?

The only way for two integers to have an odd product is each integer is odd.
For example, 1*3=3  (odd), 1 and 3 are both odd.
Or,
5*11=55, all of 5,11,55 are odd.
The sum of two odd integers is always even, so the condition of even sum is automatically satisfied when the product is odd.
Out of the four integers, there are only two odd numbers, so choose the pair to be these two odd numbers and you'd get the right answer.