The court appeared unwilling

The first issue you can tackle on this problem is the correct way to construct an idiom using "allow." "allow X" and "allow for X" are both good idioms. "allow that," on the other hand, is not correct. so you can eliminate (D). Similarly, "allow X to be possible" is awkward, so you can eliminate (E) as well.

Now we're down to (A), (B), and (C). Now we need to think about the meaning of the sentence. In particular, the connection between the opposition and the courts. The opposition has pulled for new judicial appointments, so we need an answer choice that makes that relationship clear.

In (A), "as the opposition has pulled for" does not properly make the connection. "as" is used to compare two actions, but "new judicial appointments" is not an action.

In (C), "a possibility of which" is unidiomatic.

In (B), "which" is used to create a direct connection between the opposition and the new judicial appointments. "Which" is used to begin a modifying phrase that directly describes the noun that comes before it. In this case, "which the opposition has pulled for" directly relates to the noun that precedes it, "new judicial appointments." Answer choice (B) is correct.