In the sentence that goes "The old brick house that sits on top of the hill was built during the Civil War", the adjective clause would be "that sits on top of the hill".
Adjective clauses function as adjectives to the subject which gives more detail on what the sentence is talking about. Sometimes it can be found in the beginning, or in the end of the sentence, but usually is it found in the middle of the subject and the predicate which is more convenient for writers and readers. In this case, the identified adjective clause which is "that sits on top of the hill" talks more about the old brick house and answers the question which one.
