In the last part of this sentence, we are told that the citizens' response to the Prime Minister's proposal is based on his failure to keep promises in the past. That tells us that we are looking for a negative response.
The first and fourth choices, "inspired by" and "approving of" are both very positive choices, so those two can be immediately eliminated. The phrase "adept at" means to be skilled and talented at a task, which would not have anything to do with responding to a political action. The phrase, "remiss in," means to neglect a duty. The citizens are not neglecting anything.
The only choice that makes sense in the sentence is the second choice, "wary of." To be wary of means to be cautious and not trusting. Since the Prime Minister has lied to his citizens before by not keeping promises, it makes sense that they wouldn't trust him.
The correct answer is (B).