From Ohm's law, V = IR

But R = total resistance of the circuit.

12 = 2( 3 + \(R_{parallel}\))

12 = 2(3 + \(\frac{6R}{6 + R}\))

6 = \(\frac{18 + 3R + 6R}{6 + R}\)

36 + 6R = 18 + 9R

9R - 6R = 36 - 18

3R = 18

R = \(\frac{18}{3}\) = 6 \(\Omega\)