The answer is c.independent clauses. Because 'Janet's mother wants her to be a nurse' is one idea, and 'her father wants her to be a teacher.' is another, and 'but' joins the two ideas together.
If there was no 'but' the sentence would be a run-on sentence, which is two independent clauses without any punctuation or conjunctions. If it was a run-on sentence it would be: Janet's mother wants her to be a nurse her father wants her to be a teacher.