The correct answer is D. wrote.
The sentence is in the past tense, so the correct verb must also be in the past tense. The other options are in the present tense, which is not grammatically correct in this context.
The verb “write” can be used in a number of different ways, but in this case it is being used to describe an action that was completed in the past. The speaker is saying that they were in the process of writing a letter when the person they were writing to arrived at their house.
The other options are not grammatically correct in this context. The verb “am writing” is in the present tense, which does not match the tense of the rest of the sentence. The verb “was writing” is in the past tense, but it is not the correct tense to use for an action that was completed in the past. The verb “will write” is in the future tense, which is not grammatically correct in this context.