Interpret the circuit

Since the two cells are connected together between points $X$ and $Y$ as shown, this is the standard case of two cells connected in parallel with like terminals together.
Therefore, the potential difference across $X$ and $Y$ is the common terminal voltage of the parallel combination.

Given data

For cell $E_1$: $E_1=6\text{ V}, \quad r_1=2\,\Omega$

For cell $E_2$: $E_2=4\text{ V}, \quad r_2=8\,\Omega$

Formula for terminal voltage of two unequal cells in parallel

If two cells of emf $E_1, E_2$ and internal resistances $r_1, r_2$ are connected in parallel (same polarity), then the voltage across the terminals is:

$V_{XY}=\frac{E_1 r_2 + E_2 r_1}{r_1+r_2}$

Substitute values

$V_{XY}=\frac{6\times 8 + 4\times 2}{2+8}$

$V_{XY}=\frac{48+8}{10}$

$V_{XY}=\frac{56}{10}=5.6\text{ V}$

Check options

• A: $10.0\text{ V}$ ❌
• B: $2.0\text{ V}$ ❌
• C: $5.6\text{ V}$ ✅
• D: $3.6\text{ V}$ ❌

Final answer

$\boxed{5.6\text{ V}}$