This is an assumption question. The argument might look a bit more difficult than usual because there is a long string of conditional statements, but sometimes this can actually make it easier to figure out specifically what the assumption is. Let's see if we can break down this argument:
Conc: Smoker fitness consultants cannot help clients become healthier (note the strong degree of this statement with the "cannot")
Premises: If not care self health -> cannot care client health
(let's add the contrapositive of this) If can care client health -> care self health
If do not care for client health -> cannot help clients become healthier
(let's add the contrapositive of this too) If can help clients become healthier -> do care for client health.
Interestingly, what seems to be missing here is the bit about smoking - nothing in the premises tells us explicitly about smoking, but we need that to draw the conclusion. The author seems to be saying that if a fitness consultant is a smoker, the fitness consultant does not care about his or her own health. I think in this case, where's it's so logically clear what's called for, we can afford to be quite demanding with our answer choices. Let's check them out:
(A) doesn't get to smoking (or any broader category that includes smoking), so it's out.
(B) is out for the same reason.
(C) is out for the same reason.
(D) is worth a look. This answer choice says that if not smoke -> cares about health of others. The contrapositive is if does care about health of others -> smokes. However, neither of these has a trigger (an if condition) of being a smoker, so neither the statement nor the contrapositive guarantees that if you are a smoker than you don't care for your own health or then you don't care for the health of others. It's important to see here where the directionality is. If this doesn't make sense, make sure to think about it before you move onto (E).
(E) must be our answer, so I sure hope it works out! This answer choice says if care about own health -> don't smoke. The contrapositive here is that if smoke then don't care about own health. BINGO! That's exactly what we said we were looking for. This is the answer.
This has been a great example of what I said at the beginning of this post - often these conditional logic/more formal arguments are actually easier to break down and easier to analyze in terms of identifying a specific necessary assumption. This is a really important concept, so please write in if you have specific questions about this!