B is clearly the correct answer but the question is stupid. It's not unfair (depending on the course material you had at your disposal) because a person can reasonably deduce the answer, but it doesn't really test any significant knowledge or insight.

The Missouri Compromise helped facilitate westward expansion, contributing to the map you linked. However, it was one of several such measures and other historical forces contributing to westward expansion. Hence choice "B", as it's just one of the significant factors. The other options are largely value judgments on how important the compromise was and could potentially be argued, making them ill-conceived, but in terms of the conventional "most correct" answer, B stands out.

Still, it's a stupid question because it's circular. Westward expansion led to the compromise, which led to westward expansion. It's a chicken and egg problem to suggest that the Compromise "explains" the map in question. Further, it ignores all of the underlying socio-economic factors which make westward expansion significant or interesting in the first place. It's a pointless factoid in the form of a multiple choice question (which is why I tend to hate multiple choice questions in history, but they usually aren't this bad).