The correct option is C The lady who has taught the class is a neighbour of Jill's.
A relative pronoun performs the function of a pronoun as well as a conjunction, because it refers to a noun that's common between two sentences and combines them as one sentence. The noun that it refers to is called the antecedent, and the pronoun is either immediately after the noun, or as close to it as possible, because it directly relates it to the rest of the sentence. Hence, the position of the relative pronoun determines the complete meaning of a sentence. In the statement given, "The lady" is the subject, it performs the action, the verb "taught" against the object "class". "Who" is the relative pronoun that refers to a subject, hence it should follow "lady" and not "Jill's". Option C has the correct sequence of words, and the relative pronoun is placed just after its antecedent, hence option C is correct. In A, "who" is placed after "neighbour", whereas it's supposed to be placed after "lady", hence option A is incorrect. In B, the subject has changed to "A neighbour", whereas "the lady" is the subject, and "who" only refers to the subject. Hence option B is incorrect. In D, the sentence is grammatically incorrect, 'who' is at the beginning of the sentence and is not placed after the 'lady', and the 'lady' is placed at the end of the sentence, which does not provide a complete meaning, hence option D is incorrect.