Hardly __________ entered the room when the lights went out.

The correct answer is A: had he. This sentence uses an advanced grammatical structure known as inversion, which occurs when certain negative adverbs or adverbial phrases (like "Hardly," "Scarcely," "No sooner," "Rarely," "Never") are placed at the beginning of a sentence for emphasis. When this happens, the auxiliary verb comes before the subject, similar to a question structure.

The specific structure for "Hardly" is: Hardly + auxiliary verb + subject + main verb (past participle) + when + past simple.

• The phrase "Hardly __________ entered the room" requires an auxiliary verb followed by the subject. Since "entered" is a past participle, the auxiliary verb must be "had" to form the past perfect tense, indicating an action completed just before another past action.
• "Hardly had he entered the room" correctly applies this inversion.
• The second part of the sentence, "when the lights went out," is in the past simple, which correctly follows the "Hardly...when" construction.

Let's look at the other options:

• B: he had maintains standard subject-verb order, which is incorrect with initial "Hardly."
• C: has he uses the present perfect auxiliary, which doesn't fit the past context of "went out."
• D: did he uses the past simple auxiliary, which would require the main verb to be in its base form (e.g., "Hardly did he enter..."), not a past participle.

Therefore, A: had he is the only grammatically correct option.