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Answer: (D) He asked me what time the banks opened and closed.
Explanation
In changing direct speech to indirect speech for an interrogative sentence, the reporting verb said to is converted into asked. When the direct speech begins with a question word like what time, that word acts as the connector, and no conjunction like that or if is used. The interrogative structure of the reported clause is transformed into an assertive structure, meaning the subject the banks precedes the verb. Additionally, since the reporting verb is in the past tense, the present simple verbs open and close must be changed to their past simple forms, opened and closed. The auxiliary verb do is omitted in the assertive past simple construction.