According to the teachings of the Buddhist

sameerballani wrote: I was able to mark the correct answer on the basis of parallelism, but can someone please explain what is the modifier in the sentence and its role.

which modifier?
the content of the underline is not a modifier -- in this case, both the infinitives and the -ing's are used as nouns.

in any case, parallelism is really the sole determinant of this problem.

Also, whether the additional option F is correct or not?

(f) is good enough to be considered correct, i suppose; in that sentence, the -ING constructions are gerunds, which function as nouns.
this new version is inferior to the correct answer choice, for reasons that are much too subtle and writerly to be tested on this exam; that's why it doesn't appear as an alternative option. as far as the dichotomy of acceptable vs. not acceptable, that version would be acceptable.

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by the way, why are so many posters filling up this thread with garbage posts that don't say anything other than “the answer is D”?

please don't do this -- the official answer is already in the first post!
please don't post unless you actually have something constructive to add to the discussion, so that people reading this thread don't have to waste time scrolling through posts that don't contribute anything.