A verb is used to express an occurrence, action, or state. It is the grammatical centre of the predicate in a sentence.
An auxiliary verb is a verb which gives is used in the formation of tenses, moods, tones, etc.
Option A is correct as the subject is you and infinitive is not used after like. The main verb here is like , not work. Also, the verb like indicates liking an activity, for e. g. swimming , playing, reading etc.
The other options are wrong as the subject you cannot take does as the auxiliary verb and work cannot be used to fill the second blank as like indicates being followed by a noun ( here, an activity, working).
The correct answer is A)do/working