For three decades, Waterman carried a Leica or Nikon camera and commit

parijit , Kaczet , globaldesi , and Muskan01

I am not Mike McGarry, obviously.

I am sorry that we moderators and I in particular missed these queries.

Let's dial the discussion down a bit. I understand that SC can seem really daunting. Feel free to tag me if you are waiting for an answer. If tagging does not seem to be working, send me a PM.

Speakers of British English, please read the footnote.

parijit , would you please include the source?

I will address options B and D in this post. I will follow with another post that analyzes all options quickly.

Overall impression

• AVOID FROM is not correct
If avoid is a verb, the word "from" never follows avoid.
There is no phrasal verb "avoid from."

• "Keep from" and "prevent" are synonyms. Keep from is a phrasal verb.

• The avoid/prevent distinction is not an idiom.
In this and a similar official question, the wrong verb can be eliminated because the options contain other errors.

Waterman wanted the "magical and the mundane [moments in musicians' lives]" to be remembered. OR: Waterman wanted musicians to be remembered.

Waterman took pictures because he wanted to prevent the musicians from being forgotten.

Whether "them" refers to musicians or moments in the lives of those musicians, the meaning of the sentence is clear.
Pronoun ambiguity is not an issue.

Analysis
"To keep from" is a phrasal verb that means to prevent.

Let's insert options B and D into the sentence:

(B) For three decades, Waterman carried a camera and committed thousands of musicians to film, catching the magical and the mundane in order to keep them from being forgotten.

(D) For three decades, Waterman carried a camera and committed thousands of musicians to film, catching the magical and the mundane in order to avoid them from being forgotten.

• Option D: errors in grammar and meaning

The phrase avoid them from being forgotten is ungrammatical and nonsensical.

(1) Verb misconstruction. Do NOT use "avoid" with "from"

Avoid is never followed by from in this construction: avoid ___ being forgotten

Avoid can be followed by
• a gerund: They avoid swimming.
• a gerund phrase: They avoid swimming in polluted water.
• a noun: He avoids conflict.
• a pronoun: Poison ivy plants cause itching; try to avoid them.

"Avoid from" is wrong. Options D and E incorrectly imply that avoid from is a phrasal verb or that avoid is a verb that can take the preposition "from."

Avoid from is not a phrasal verb. Avoid from does not exist as a verb or verbal of any sort. Avoid is not like keep from.

Correct: He closed the window to keep the rain from ruining the curtains.
WRONG: He closed the window to avoid the rain from ruining the curtains.

Avoid does not take the preposition "from."Prevent is a verb that DOES take the preposition from.

Correct: The Washington, D.C.-Moscow hotline prevents disputes from escalating.
WRONG: The Washington, D.C.-Moscow hotline avoids disputes from escalating.

"Avoid from" is incorrect 99% of the time, and incorrect 100% of the time if avoid is the verb.

(2) The meaning in D is garbled. To avoid them means to stay away from them.

To "avoid them" means to stay away from whomever "them" may be: bullies, angry wasps, demons, xenophobic authoritarians.
Waterman took pictures, but not because he was avoiding musicians.

Avoid them from has no meaning.

Examples of the usage of keep from, prevent, avoid

Correct: Please put oil in the cars to keep them from breaking down.
Correct: Please put oil in the cars to prevent them from breaking down.
Correct (though awkward): Please put oil in the cars to avoid their breaking down.
Correct (not awkward): Please put oil in the cars to avoid breakdowns.
NEVER: Please put oil in the cars to avoid them from breaking down.

Official question resemblance

If you are not a native speaker and picked (D), try not to worry and please see the footnote below.* If you are a native speaker who picked (D), I think you must have misread the option.

Avoid, prevent from, and keep from are tested in this Official GMAC question, but you do not need to know

The sentence in this question is taken from this article in Smithsonian magazine. The prose is a good example high-level writing. HINT Dick Waterman is fascinating.

In an indirect way ("keep from" is a synonym of "prevent"), this question tests the idiom Prevent X from Y (prevent the musicians from being forgotten).

Finally, do not worry too much. We know now that avoid is not coupled with from.

I hope that helps.

*Many non-native speakers have been trained in British English. I briefly surveyed the common usage of avoid in British English. "Avoid" seems to stand in for "prevent" frequently in common parlance and journalism. U.S. English is different. Avoid stands in for prevent quite rarely, and compared to British English, very rarely.
You probably do not need to understand the subtle semantic differences between avoid and prevent (or "keep from") that are created by context. If you have been trained in British English, however, you may need to be careful. Do not automatically select "avoid" over "keep from" or "prevent" because you have read or heard "avoid" more often.