The correct answer is A. The teacher asked me, “Why were you absent yesterday?”
The teacher is asking about a past event, so the past tense is used. The teacher is also asking about a specific day, so the day is named.
B is incorrect because the present tense is used. The teacher is not asking about a current event, but about a past event.
C is incorrect because the day is not named. The teacher is asking about a specific day, so the day should be named.
D is incorrect because the teacher is not asking about a yes or no question. The teacher is asking about a reason for an event, so the question should be open-ended.