The correct option is D did / do
The tense of a sentence denotes a time, whether it is the time now (present), time then (past) or the time to come (future). The verb of a sentence has most to do with the tense. In the given sentence, we need to fill in a word that determines the correct tense. The action here was performed and completed in the past, we know this as it's given "last week". From the options, 'did, do' is the most suitable set of verbs, where 'did' is the helping verb that determines the tense of the sentence as the past "last week" and 'do' is the main verb in the past tense, that refers to 'performing an action', 'to do work', hence option C is correct. 'Were, do' is an incorrect pair, as 'were' is used in the past continuous tense, and is followed by 'doing' which is also in the past continuous tense 'were you doing', hence option A is incorrect. 'Did, did' is grammatically incorrect, because one of them is required to be a helping verb, as the sentence is in the past tense, 'did you do' is the correct form, hence option B is incorrect. 'Do, did' is incorrect as well, as 'did' being a helping verb precedes the main verb, not vice versa. The sentence is in the past tense, if it were in the present tense it would go like this 'What work do you do?', hence option D is incorrect.