The current source provides $I_0=1A$ current through the left branch (upward), while the voltage source provides $V_0=2V$ across all three components. The current through $R$ is $2V/3\Omega=2/3A$ (downward), the current through the voltage source is $I_v=1-2/3=1/3A$.

When the polarity of $V_0$ is reversed, we have

• Power dissipated by $R$: $3\times (2/3)^2=4/3\;W$.
• Power delivered by voltage source: $2\times (1+2/3)=2\times 5/3=10/3 W$
• Power received by current source: $1A\times 2V=2W=6/3\;W$

$$\frac{4}{3}+\frac{6}{3}=\frac{10}{3}$$