What will be the amps of a 12v 2amp circuit if there is a 12ohm resistor on it?

The formula you are looking for is I = E/R. Amps = Volts/Resistance.

If you say it is normally a 2 Amp circuit, it normally draws 2 amps.

Therefore the original resistance offered to the 12v battery is 2/12 = 6 Ohms.

If you then connect a 12 Ohm resistor in series, they are added, so R = 18 Ohms.

Now if you put 12v across this circuit it will draw 12/18 = 0.66 Amps.

Or

If you just put a 12 Ohm resistor across the 12v supply it will draw 1 Amp.

If the circuit is protected by a 2 Amp fuse, it will not blow, but the resistor will get hot.