The potential difference $\left(V_{\mathrm{A}}-V_{\mathrm{B}}\right)$ between the points $A$ and $B$ in the given figure is

Complicated circuits with multiple potential points and batteries can be easily solved using Kirchhoff's laws.

Consider applying Kirchhoff's voltage law (KVL) to the given circuit.

$V_{\mathrm{A}}-V_{\mathrm{B}}=\left(2\times 2\right)+3+\left(2\times 1\right)$

$=4+3+2$

$=9\mathrm{ V}$.