C is the only right answer. Sometimes people write "guilded" when they mean "gilded," but if you mean an item that has been thinly coated and adorned with something shiny or valuable, you're talking gilding.

The others:

• A: Really the phrase is "just as soon." Meaning you'd be just as likely (or more likely) to do the new thing you're suggesting. "Just assume" doesn't make grammatical sense the way some people try to use it.
• B: No, they don't mean that your brain is covered in hair when you come up with stupid ideas. They're saying your brain is that of a hare. Those li'l bunnies are excitable and not as clever as ol' Bugs.
• D: No-no, guys. I understand you think "peaking interest" refers to your interest growing to its pinnacle, but that's not how the phrase works. It's actually "piques their interest." It's from the French word meaning "stimulate."