The correct answer is A. He asked me what I was doing.
The sentence “He said to me, ‘What are you doing?” is in the past tense. This means that the action of asking the question happened before the time that the sentence is being spoken. In this case, the speaker is asking the listener what they were doing at a specific time in the past.
The other options are incorrect because they do not reflect the fact that the action of asking the question happened in the past. Option B, “He asked me what am I doing,” is in the present tense. This would be correct if the speaker was asking the listener what they are doing right now. Option C, “He said to me what I was doing,” is in the simple past tense. This would be correct if the speaker was simply stating what the listener was doing at a specific time in the past. Option D, “He asked me what I am doing,” is in the present tense. This would be correct if the speaker was asking the listener what they are doing right now.
In conclusion, the correct answer is A. He asked me what I was doing.