The president won the election because of the ____ speech he made, which won him people's trust successfully.
Neither choice is perfect, but I'd argue the correct answer to this question is a. astonishing.
Reason 1: It is highly unlikely that you would describe an entire speech as plausible. A specific individual claim (or campaign promise or inspiring story) from the speech might be plausible or not, but it's just not a term that would normally be applied to an entire speech, except perhaps if the entire speech was one long single topic or single argument (very few political speeches are).
Reason 2: "Astonishing" is much greater praise than "plausible", and therefore much more likely to win someone's vote/trust. In fact, "plausible" is hardly praise at all, it's more of a tepid acknowledgement that there is some chance the claim/fact might not be totally wrong. (This is a bit of an exaggeration, and certainly not something you'd see in the dictionary definition, but I'm just trying to put into words how it is used/perceived.)
I think the fact that the speech is described as something that won the candidate the election, that "astonishing" is much more likely to be correct.
Possible counter-point: A speech being "astonishing" could cause people to like him or to support him or whatever, it is a little harder to see how it would cause people to trust him, since those don't really have much to do with each other. "Trust" and something being "plausible" are at least talking about the same kind of thing (truth/falsehood). But if that's the point the writer was trying to make, I think they would describe it a different way.