The current in resistance $R_3$ in the given circuit is

Current through $R_1$ and $R_2$ comes out to be zero (potential difference = 0)
Current through,

$$\begin{gathered} R_3=\frac{Net emf}{Total resis\tan ce} \\ =\frac{(4+3+2)-(2+3+2)}{3} \\ =\frac{2}{3}A \end{gathered}$$