First, let's be 100% clear on what the passage's argument is:

Athletes should drink regular Cheetah sweet (which contains sugar) instead of Cheetah Sweet's zero calories drinks because the chemicals in Cheetah Sweet's zero calorie drinks are deleterious (a fancy word for harmful).

We want to find an assumption on which the argument depends. We can use the negation test to prove answer choices correct or incorrect: in other words, would the argument still be true if the answer choice was NOT true. Let's look at answer choices A and D, since those are the ones you're struggling with.

(A). The chemicals affect anyone who drinks Cheetah Sweet's zero calorie line.
Let's negate answer choice A: what if the chemicals DID NOT affect any who drinks the zero calorie drinks. We know that the argument is only about whether or not athletes should drink the zero calorie line. So if non-athletes are not affected by the zero calorie drinks, it doesn't affect the argument! We don't need to know that everyone is affected, just athletes. So A doesn't need to be true. Eliminate.

(D).Sugar does not have a more deleterious effect on the body than the chemicals in question.
Let's negate answer choice D: what if sugar DID have a more deleterious (harmful) effect on the body than the chemicals in the zero calorie drinks. This would means that drinking regular Cheetah sweet would be even more harmful that drinking Cheetah Sweet's zero calorie drinks. This means that athletes should NOT drink regular Cheetah Sweet over Cheetah Sweet's zero calorie drinks. So the argument is disproven if D is not true. This means that D must be true for the argument to be true - the argument depends on the assumption in D. This must be the correct answer.

We can go through a similar negation process for the other wrong answer choices as well.