This about number properties - specifically even/odd which is often best tested by pluggin in numbers when you don't knwo the rule. But this question is badly written because if you plug in 1 for each of the answers you see that none of them have to be true. Even if you assume the question says if a and b are distinct odd integers then you have to make them different and you see that if you plug in 1 and -1 they are all false - can you give me the source of the question?

I think the question should state if If a and b are positive odd integers, then only c holds true, try plugging in 1 for all choices then only c holds true

c doesn't work if they are both 1 becuase 1(2)(2) - is not divisible by 8.

problems says which option is necessarily true.
so if we look at answer choices then except D other may or may not be true.
So i think option D is correct one.
options:
A) is false as ab will always be odd
B) in ab(a-1)(b-1), there are two even numbers and to be divisible by 8 there has to be at
least 3 even nmbers( three 2's), so this may or may not be correct
C) similar reasoning as B , this may or may not be correct.
D) is correct, always divisible by 8
E) similar reasoning as B & C.