The exchange that I'm attempting to transfer Monero out of requires a Payment ID. But Monero GUI 0.12 doesn't have Payment ID's anymore.
It sounds like the exchange is asking for a 256-bit payment ID.
If you are sending funds to your own GUI wallet, you will have no problem figuring out who sent you the payment. Therefore you don't need to use a unique payment ID.
If the exchange does not let you leave it blank, you simply enter any 64-character hex sequence, such as just 64 zeroes.