How can I find the value of these resistors in this power supply?
R6 is the gate stopper resistor, so 22R would be a good start. R12 is in the current sense circuit, so my guess is around 1K. As others have mentioned, there’s collateral damage. The 3842 controller chip is most likely fried. There may be a zener in the gate circuit that is fried and so on.
Power supplies using the ucc3842 tend to follow much the same pattern. The datasheet has a generic circuit that might give some hints.
When you replace the low ohm current sense resistors - don’t use wire-wound types due to inductance.