The correct option is B While I drove to my parents' house
An adverb clause is a group of words containing a subject and a verb,
and it functions as an adverb, by modifying an adjective, verb or an
adverb. Adverb clauses generally begin with a subordinate conjunction
(since, because, while, etc.).
Option B is correct because it is an
adverb clause of time, 'while' is a subordinate conjunction that refers to two events that happen at the same time.
Option A is incorrect because it is a phrase, not a clause.
Similarly, option C is incorrect because it
is a phrase, not a clause.
Option D is incorrect because the answer lies in B.