Hello!
Thank you for your question! Let's break down each answer, and determine what is right/wrong about each one:

Environmentalists report that much of the increase in levels of dangerous mercury ingested by Americans is due to high concentrations of the element in tuna and other fish.

A. much of the increase in levels of dangerous mercury ingested by Americans is due to high concentrations
This one is the right answer because it correctly uses "much of" instead of "many of," and correctly uses "is due" instead of "are due."

B. much of the increases in dangerous levels of mercury that Americans ingest are due to high concentrations
This one is wrong for a couple reasons. First, it moves the word "dangerous" from in front of mercury to in front of levels. In this case, the levels aren't what's most dangerous - it's the mercury. Second, whenever you use the phrase "much of..." it should be followed by a singular word. In this case, it's followed by a plural "levels," which also leads us to incorrectly say "are due" later on.

C. much of the dangerous increases in the level of mercury Americans ingest are due to a high concentration
Just like B, the problem with this sentence has to do with where the word "dangerous" is located. The mercury is what is dangerous, so the adjective "dangerous" needs to go before mercury, not increases.

D. many of the increase in dangerous levels of mercury ingested by Americans is due to high concentrations
This one also has the problem of putting the word "dangerous" in the wrong place. Also, the phrase "many of the..." needs to be followed by a plural word, and in this sentence it's followed by the singular "increase."

E. many of the levels of increase in dangerous mercury ingested by Americans are due to a high concentration
This one is very awkward to read and understand. At face value, it suggests that there are "many levels of increase," rather than just one (the level of mercury ingested by Americans is just one thing). That, and saying "many levels of increase" just sounds odd.

I hope this helps! I'm available if you'd like any follow up!