Thanks for that bit of cultural history. I learned something new today.
An important "palace"? Seriously. That's redundant, if you're dealing with palaces [coming from someone who doesn't :D]. I think in this case, the better translation would be "building" which I saw as a hint. I used it and it was still marked as correct, but I think that palace would be a lesser used translation here.
The hint writer knew more than the translator here. Importante is an option for 'great'. This looks silly until you add 'palace', when it becomes normal English usage. Dictionaries agree. Duo rejects it.
So edificio is rather a building where there are offices? and palazzo is a building with apartments. È vero?
I used "a big palace" and was marked as incorrect. One of the definitions of "importante" is "big."
In American English (at least in my experience), the word "palace" refers (in a literal sense) only to a place where kings and queens live. Sometimes large houses are called "palaces" but only in an ironic/over-the-top complimentary way: "This place is [like] a palace." We refer to very large private houses as mansions. And tacky, overly ostentatious, architecturally incongruous mansions are called "McMansions."
Is the word 'importante' also used as a way to imply a building with a lot of presence? It's used this way in Spanish as a sort of slang word, e.g. "vive en una casa importante" - he lives in a really cool/big house. It's the same in Italian?