Answer: The answer is: B) wouldn't be able to/had broken.
Explanation: It can't be A because it wouldn't make sense for him to say "won't" when his car broke down accidentally, because it makes it sound like he's choosing not to because he doesn't want to. It also can't be C because it wouldn't make sense for the sentence to say, "because the car has broken down" when the rest of the sentence is in past tense, because the word "has" indicates that is just now happened. And it also can't be D because, well for obvious reasons, like, first of all, "breaks" is not in the correct tense or context, and, it's not that he shouldn't pick the kids up from school, he just can't/isn't able to.