I assure you that it's possible. To give you a hint without giving everything away: the guess of the first person must be derived from the colour of all other person's hats.

You could think of it as a puzzle in coding theory, and it's not implausible. If you sum up the number of hats that each person sees and the number of guesses they hear, you'll note that everybody has 9 bits of information available. And they're supposed to make 9 correct guesses. It adds up.

Another hint would be to think of the case of 3 persons first. That can be done with patient case analysis, and it's likely to get you an idea for generalisation.