(Ah, here's my initial reply in another window hiding from me)
Well, firstly, the resistor is unlikely to be the only thing that's failed. You need to determine why that resistor failed so that when you replace it it doesn't simply fail again.
As for its value, it's 0.?2 ohms. The ? might be nothing, an 8, or a 2. I would doubt it is 0.02 ohms. The other 2 guesses are based on the resistor having an E12 value.
I also note that there is no sign of another digit between the 0 and the 2. It looks to me that if there were a 2 or an 8 there, you'd see the top of the digit.
My best guess is that a 0.22 ohm resistor would be a suitable replacement. My guess is that it's between 1/2 and 1 watt.
I also note that it appears it is not intended to get hot in operation as it appears to have been mounted hard on the board and there is no sign of localised long term heating (although that may not be easily visible on a fibreglass board).
I would look at what power components are connected to this resistor and see if any of them measure short circuit.