Mrs. Roy is a silly woman who books . . . . . . . . anyone who doesn’t own a car.

The correct answer is A. on.

The word “books” can be used in a number of ways, but in this context it means “to make a reservation for”. So, Mrs. Roy is a silly woman who makes reservations for anyone who doesn’t own a car.

The other options are not correct because they do not make sense in the context of the sentence.

• “Down” could mean “to defeat” or “to put down”. However, it does not make sense to say that Mrs. Roy defeats or puts down anyone who doesn’t own a car.
• “Down on” could mean “to look down on” or “to be critical of”. However, it does not make sense to say that Mrs. Roy looks down on or is critical of anyone who doesn’t own a car.
• “Down off” is not a grammatically correct phrase.