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 B is correct as the subject is singular/plural and the present simple tense is used for a present state, habits,routines, jobs, hobbies or expressing possession, generalizations, scientific statements.
The other options are wrong as smoke can not 's' as it comes after I and my teacher is not plural.
The correct answer is B)smoke/doesn't