Weigh four against four. If they balance, the fake is in the other four, and two more weighings against good coins find it. If they tip, the second weighing moves some suspects across the pans and swaps others for good coins, which leaves three or fewer, and the third settles it.
It works because a balance has three outcomes, not two: three weighings give 27 results, enough to cover twelve coins that could each be heavy or light.