"What do you like?"
That would sound like "What does the country/state like?", because "państwo" used this way means "country/state". (not a 'state' as in one of the United States, mind you).
"państwo" as Formal You is plural, "Co państwo lubią?" (or "Co Państwo lubią? if you actually write directly to them, and not just in a Duolingo comment)