The 4th Year Party Hat was a rare head item in Club Penguin. All players could've obtained it for free in the Coffee Shop during the 4th Anniversary Party. In order to obtain it, players had to mouse over a pinata twice, which would cause it to fall.
If a player wore this, or any of the other anniversary hats released before the seventh anniversary hat, and went to the Fire Dojo or Water Dojo, Sensei would've commented, "I see you're wearing an Anniversary Hat. I like pointy hats."