Why is it that all of these questions you post seem to have multiple correct answers? Whoever's giving you this test is a sadist. I'd avoid A simply because it's too long, poorly parsed, and a bit ambiguous. "Well enough" is an odd phrase to use in this sentence, "undertaken" is not a word that should be used to refer to a studied subject (it's used more for a brief ordeal), and "to do the speaking" is just clumsy. B sounds mostly fine to me. The only thing I'd change is the "in terms of" part. I'd say it as "in regards to the subject" instead. "In terms of" is just slightly wrong in a way I can't even fully express, but it's also not something I'd ever be confused by or look at someone weirdly for saying. C actually sounds just great. The only problem here is that there should be a hyphen to connect "well" and "acquainted". I suppose the only reason this might be wrong is if you're supposed to convey a particular MEANING, because unlike the other three options, C means something different. The other three describe an expert on the subject; C describes an informed layperson who knows more than average about the subject. IF you're supposed to be choosing a sentence that is grammatically and organically correct AND is talking about an expert, then C is wrong but ONLY because it's not properly describing an expert. In terms of natural flow of language, it's the best of the four. D is wonky due to that weird "close awareness" thing. I've never heard those two words put together in my life. They make sense to me, but they're just not natural at all. So my answer would be either B (if you are required to be talking about an expert) or C (if the only requirement is natural sentence structure).

The problems with sentence A is the word order. It doesn't sound natural. It would sound better like this: "The speaker is someone who knows the subject about which he has undertaken to do the speaking well enough." I don't see anything wrong in sentence C (except that all the sentences need a period at the end).