The correct answer is D. she is doing.
The question is “What is she doing?”. The answer is “She is writing a letter.”. This means that the action that she is doing is “writing a letter”. The verb “writing” is in the present continuous tense, which is used to describe actions that are happening at the moment of speaking. The correct answer is therefore “she is doing”.
The other options are incorrect because they do not describe the action that she is doing in the present continuous tense. Option A, “does she do”, is in the simple present tense, which is used to describe actions that happen regularly or habitually. Option B, “does she”, is also in the simple present tense. Option C, “is she doing”, is in the present continuous tense, but it is not the correct answer because it does not agree with the subject of the sentence, which is “she”.