D) are you doing
The phrase 'this evening' in the sentence suggests that the question has been asked in the present. Thus, the answer must be a phrase in the present tense. Also, since the answer for the blank is part of a question, it must be in interrogative form.
Option A is incorrect. 'you will do' is not an interrogative phrase and so, it cannot be used to ask a question.
Option B is incorrect. 'do you' itself is a grammatically incorrect phrase as it does not contain a main verb. Thus, it cannot be the answer.
Option C is incorrect. 'you doing' is not an interrogative phrase as it does not have an auxiliary at its beginning. Also, since it lacks an auxiliary verb, using it will make the sentence grammatically incorrect.
Option D is correct. 'are you doing' is an interrogative phrase and can be used to ask a question. Further, it is in the present continues tense and so, it justifies the question being asked in the present. It asks the subject what he/she will be doing this evening.
