Qual è la differenza tra fantastic e fantastically and why can’t I say “it looks fantastically “ if it’s an adverb ?Sentiti libero di rispondere con un esempio.

As you note, fantastically is an adverb meaning extraordinarily well. So you would not say of something It looks well, you would say It looks good. You are describing "It," not modifying
"looks." (or describing the manner in which it looks.)
That is why you would use fantastic, which is an adjective, meaning extraordinarily good.
It looks fantastic.
When you are modifying the verb, you would use fantastically.
He performs fantastically. (You are describing the manner in which he performs.)
His performance looks fantastic. (You are describing his performance.)