Two cells are connected between points A and B as shown. Cell 1 has...

Equivalent internal resistance of two cells in parallel is ${r}_{eq} = \dfrac{{r}_{1}{r}_{2}}{{r}_{1} + {r}_{2}} = \dfrac{3 \times 6}{3 + 6} = 2Ω$

Equivalent emf of given cells

${E}_{eq} = \left(\dfrac{{E}_{1}}{{r}_{1}} - \dfrac{{E}_{2}}{{r}_{2}}\right){r}_{eq} = \left(\dfrac{12}{3} - \dfrac{6}{6}\right)2 = 6V$

Given: $R = 4Ω$

The circuit can be redrawn as shown below.

Current through resistor $R$ is $I = \dfrac{6}{2 + 4} = 1A$.