Because ethylene dibromide, a chemical used to fumigate grain, was

Sure! I can give this a shot.

Ok, this questions asks for the assumption. Lets find the premises and conclusion first:

Premise 1: Because ethylene dibromide, a chemical used to fumigate grain, was blamed for the high rate of nerve damage suffered by people who work in grain-processing plants, many such plants switched to other chemical fumigants two years ago.

Counter premise: however, the percentage of workers at these plants who were newly diagnosed with nerve damage has not dropped significantly.

Conclusion: Therefore, either ethylene dibromide was wrongly blamed or else the new chemicals also cause nerve damage.

Now, we have to find the assumption on which the conclusion, i.e ethylene bromide was wrongly blamed, is based.
Maybe a diagram will help?

eth bromide---> caused problems
.
.
After 2 yrs
.
.
Switched to another chemical---> problem still exists!

So--> ethyl bromide is NOT the root cause of this problem

Now, lets look at the answer choices: (Remember, we have to focus on the conclusion, i.e ethyl bromide is not the root cause)

A. If the new chemicals cause nerve damage, the nerve damage caused would be different from any nerve damage that ethylene dibromide may cause. Not true because this tells us about the new chemical and a if scenario. But we already know that the new chemical causes nerve damage. Besides this wont help us conclude that eth bromide is NOT a cause for damag

B. There are no chemical fumigants that are completely safe for workers in grain processing plants.
This is too broad to claim that no chemical is safe

C. If ethylene dibromide causes nerve damage, it does not take two years or longer for that damage to become detectable.
If you remember the premise, it says that after 2 yrs workers switched to a new chemical. Which means that it takes less than 2 years to detect the damage caused by ethylene bromine. So this is the correct answer choice
Another way to prove this is the correct answer is to negate it. If we said that it takes MORE than 2 years for ethylene bromine to be detectable, then we cannot prove if it was ethylene bromine or the new chemical that caused the damage, since we already switched to the new chemical within 2 years. So this statement is a good assumption
D. Workers at grain-processing plants typically continue to work there even after being diagnosed with nerve damage.
This would actually weaken the argument because if the workers worked, there is no way of proving which chemical caused the damage
E. Workers at grain-processing plants that still use ethylene dibromide continue to have a high rate of nerve damage.
Not an assumption, because it does not directly support the conclusion which is: ethy bromine is NOT the root cause fot the damage.

Hope this helps.