The correct option is B How does he write?
A question needs to be framed for which the underlined part, "as well as he speaks" is the answer.
So, the question should ask 'how' well he writes, the response to which is in comparison to how he speaks.
Option B: 'How does he write?' asks how he writes. The underlined part 'as well as he speaks' is a suitable response for the question 'how'. It answers by comparing similar qualities.
(The given sentence says that he writes well, the same as he speaks well.)
Hence option B is correct.
Option A: The question asks 'what'. However, the response is not appropriate for 'what' he does. So, the question is ambiguous. Hence, this question isn't appropriate for the underlined part.
Option C: This question asks about which person 'who'. The underlined part does not answer this question. It does not answer to 'who' writes as well as he speaks, but 'how'.
Option D: The underlined part does not answer the question 'how he speaks'. The response sounds incomplete for this question, because 'as well as' denotes a comparison with something else.
Instead, the response is for a question that asks 'how he writes'.
Hence options A, C and D are incorrect.