Topic: Affirmative Negative Agreement,

Best Answer Explained in Below-:

The sentence "He does not like vegetables, neither ... I." requires an auxiliary verb that agrees with the negative construction and effectively conveys that the speaker shares the same sentiment as "he."

When restructuring the sentence using "neither," we are looking for an auxiliary verb that correctly negates the speaker's feelings about vegetables. The options provided—"like," "prefer," "do," and "does"—each have different implications:

A) "like" would not work here because it does not align with the negative form of the previous clause.
B) "prefer" alters the intended meaning by implying a different level of preference rather than simple agreement on dislike.
C) "do" is the correct choice. It completes the negative construction initiated by "does not," maintaining the parallel structure of negation. The sentence thus reads: "He does not like vegetables, neither do I," which accurately expresses that the speaker also does not like vegetables.
D) "does," while it follows the correct subject-verb agreement with "he," creates an incorrect structure since it cannot be used with "I" in that negating context.

Therefore, "do" is the only option that maintains the syntactic and semantic integrity of the sentence, making it the correct answer.