"Eulogize" means to praise someone or something highly, often in a formal way, such as in a speech that celebrates a person's achievements or qualities. To find its antonym, we need a word that means the opposite, that is, to find fault with or speak negatively about someone.
"Criticize" means to point out faults or express disapproval, which is the direct opposite of praising someone. This makes option 2 the correct antonym of "eulogize".
Option 1, "extol", actually means the same as eulogize, to praise enthusiastically, so it is a synonym, not an antonym, and can be ruled out immediately. Option 3, "emulate", means to try to match or imitate someone's achievements, which is unrelated to praising or criticizing, so it does not work as an antonym either. Option 4, "amulet", is not even a verb related to praise or blame at all; it is a noun meaning a charm worn for protection, and it appears here mainly as a word that looks similar to "emulate" to test careful reading. None of these three options carry the meaning of criticizing or condemning, so "criticize" remains the only correct antonym.