Answer
$P =0.375W$
Work Step by Step
Applying kirchofs law
$ 12V- 0.25A * 12\Omega - 0.25A* 6\Omega -6V - 0.25A*R =0$
$12V -3V - 1.5V -6V = 0.25A*R$
$R= 6\Omega$
Power dissipated is
$P = I^2 R = (0.25)^2 * 6 W$
$P =0.375W$
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