Whenever my students ask for new words, I insists them to look for good…

Concept: The verb insist does not take the pattern [object + to-infinitive] — you cannot say "insist somebody to do something." Standard English requires either a that-clause ("insist that he go" / "insist that he should go") or "insist on" plus a gerund ("insist on his going"). Separately, "look up" a word means to consult a reference source for it, while "look for" means to search for something; the two do not combine into "look up for." Finally, a subject in the first person singular ("I") always takes the base form of a present-tense verb, never the -s form.

Application: The given sentence — "Whenever my students ask for new words, I insists them to look for good vocabulary words in the dictionary" — has two problems: the subject-verb form "insists" needs to become "insist," and, separately, "insist" is already followed by an object ("them") and a to-infinitive ("to look"), which is not a pattern insist supports at all, regardless of which verb form is used. Checking each offered rewrite against both rules: every one of them corrects "insists" to "insist," but every one of them also keeps "insist them to," the very construction that insist cannot take. Two of the three additionally replace "look for" with the non-existent phrasal verb "look up for," instead of the genuinely correct "look up." This exact "insist ... to" slip is also one of the most frequently tested traps in sentence-correction exams.

Cross-check — why each rewrite still fails:

• "Whenever my students ask for new words,I insist them to look it up for good vocabulary words in the dictionary." still has "insist them to" (the unsupported object-plus-to-infinitive pattern), and its pronoun "it" doesn't agree with the plural "new words" it's meant to stand for, while the trailing "for good vocabulary words" then redundantly restates the same thing.

• "Whenever my students ask for new words, I insist them to look up for good vocabulary words in the dictionary" fixes the subject-verb form but keeps "insist them to," and blends two different phrasal verbs into the non-existent "look up for."

• "Whenever my students ask for new words,I insist them to look up for good vocabulary words in the dictionary." has the same "insist them to" and "look up for" problems as the version above.

Result: Because none of the three rewrites removes the "insist + object + to-infinitive" error — and two of them introduce the non-existent "look up for" in its place — none of the offered corrections is a genuinely correct sentence. The right choice is that none of the given alternatives fixes the sentence.