First, I divide the 12 coins equally and weigh them. I will again divide to equal numbers whichever half is heavier and weigh them. Now, I'll isolate the 3 remaining coins that are heavier. I'll label them 1, 2, and 3. I'll choose two coins to weigh. If I weigh 1 and 2, and one is heavier, then that'll be the fake coin. If 1 and 2 are equal in weight and are balanced, then the 3rd coin is the fake coin.

It was a fun puzzle game. Thanks Hive account@nafion.