why my power calculation for this resistor is wrong?
simulate this circuit &ndash; Schematic created using CircuitLab

Since the 4 Ω has the voltage signs marked + on the right then let's have current, i, flowing right to left through it and anti-clockwise through the circuit. Starting at R1 and going anti-clockwise we get:

4i + 16 + 2i + 12i + 6i - 4 = 0
24i + 12 = 0
i = -12 / 24 = -0.5 A


In fact, the current is running clockwise.

Now you have the current you should be able to work out the power in the 6Ω resistor.

I think your problem was falling for the 'trick'. The + and - signs are reversed on the 4Ω resistor. You calculated voltage drop on the 2Ω correctly but did it with the opposite sign on the 4Ω because the question deliberately misled you.