HiCustomer and welcome to JA!
The answer is no. There is no way for all 12 players to play with every other player in just 4 rounds.
I'm not sure if this is a math problem or if you are actually having a golf event, so here is a detailed description of why that is the case:
Here is the "most" optimal schedule for players A1, A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, and C4:
I hope this helps. Let me know if you have any questions,