It is now time to go after Hoyt directly, so fast travel to The Compound and talk to Sam. He mentions that there’s no going back after accepting to continue with the mission, so if you have anything to do, do not proceed. If you’re ready, tell Sam you’re good to go and proceed with the mission.
You now have to play a hand of poker. At the end of the hand, Hoyt will end up stabbing Sam, and reveal he knew you were Jason Brody all the time! When given the prompt, bet with your life. You’ll end up winning that game, but will have to play another. This time, you will lose and Hoyt will end up cutting off one of your fingers.
You’ll now be in a special place where it’s just you and Hoyt. There will be quick time events, with the buttons you have to press corresponding to the position. These QTEs move pretty fast and if you fail, you will die and have to restart from the first QTE. The last QTE will bring about Hoyt’s death and after a short scene, you automatically start the next mission.