I'm sorry to hear your game is crashing while trying to launch. Far Cry 4 is now relatively older, so it's more unlikely, but I still recommend that you make sure the PC you are playing the game on meets minimum requirements. If it does please try running the game as administrator, running Uplay as administrator, and verifying your game.
If you continue to see a black screen, please do a clean install of your graphics drivers (Nvidia / AMD). After you restart your PC again please try the game. If you continue to have troubles I recommend reaching out with your system files so that we can see if we can determine the cause of the crashes.