Her style is quite lucid, we always wanted to make her fashion idol.

Concept

A sentence-correction / vocabulary-in-context item like this tests two things together: (1) picking the replacement word that preserves the meaning of the word it replaces, and (2) fixing any structural errors in the sentence -- such as a comma splice joining two independent clauses (which needs a semicolon, full stop, or conjunction instead of a bare comma) and a missing possessive determiner before a noun phrase.

Applying it here

The word "lucid" describing someone's style means clear, easy to understand -- the kind of quality that would make people want to look up to her. Among the offered replacements, only "transparent" preserves this "clear, easy-to-understand" meaning. The original sentence also has two structural faults: the comma in "...lucid, we always..." creates a comma splice (two independent clauses joined only by a comma), and "make her fashion idol/mentor" is missing the possessive determiner "our" before the noun phrase. A correct version needs a semicolon in place of that comma AND the word "our" inserted. (Here, "transparent" is used in its "clear, easy-to-understand" sense -- the sense that dictionaries and thesauruses list as a synonym of "lucid" -- rather than its literal "see-through" sense; the surrounding context, wanting to look up to her as a mentor, supports this reading.)

Why the other options are incorrect

• "Witty" means clever or amusing, not the "clear, easy-to-understand" quality the original word conveys, so this word choice changes the sentence's meaning; this version also still uses "wanting" instead of "wanted" (a tense mismatch) and still joins the two clauses with only a comma.

• "Provoking" means causing a strong or defensive reaction, which is the opposite of the "clear, easy-to-understand" quality the original word describes, so this substitution changes the intended meaning.

• Assuming no correction is needed overlooks that the sentence still joins two independent clauses with only a comma and is missing a possessive determiner before the noun phrase -- a fix genuinely is required.

Only the option that supplies a true synonym of the original word AND fixes both the comma splice and the missing possessive determiner resolves the sentence correctly; the additional swap from "idol" to "mentor" in that same version is a secondary wording change that introduces no error of its own, so it does not affect this determination.