The correct option is
C down
The phrasal verb, "break down" means "to stop functioning" or "to undergo chemical decomposition". It also means "to cry". The sentence, "Her car broke down again" means, that her car stopped functioning again. The word, 'again' suggests that this is a recurring event and not the first time. In order to address this, the next sentence follows i.e. "She should buy a new one". Hence, option B is correct.
The phrasal verb, "break up" means "to come to an end"/ "gradually divide into smaller pieces". A car cannot come to an end. Similarly, it cannot get divided into smaller pieces again and again. Both the verbs do not apply to car. Hence, option A is incorrect.
The phrasal verb, "break-in" means "to interrupt when someone is speaking". It also means "to enter a building illegally with the intention of stealing". Both these verbs cannot apply to a car. Hence, option C is incorrect.
The phrasal verb, "break off" means "to separate from a larger piece" or "to end a relationship". A car cannot separate from a larger piece/end a relationship. Both these verbs don't apply to a car. Hence, option D is incorrect.