The headlamps won't get 12V across them, because the internal resistance will steal some of the voltage. You've shown that the voltage across the battery's terminals is only 8V - i.e. the battery behaves effectively like an 8V battery.
So only 8V are available to be across the lamps. With this in mind, and using the resistance of the lamps, work out the power the lamps will exhibit.
On a side note, it's a bad idea to use the same symbol (P in your case) for two different things. It can confuse examiners and lose you marks.