The question refers to a circuit diagram, but the figure is not provided in the prompt.

Without the circuit figure, the voltage across the $15\,\Omega$ resistor cannot be derived uniquely from first principles, because it depends on how the resistor is connected with the rest of the circuit.

However, since the stored correct answer is given as $6$, I can only note the following:

1. The asked quantity is the voltage drop across the $15\,\Omega$ resistor.
2. The stored correct answer says this voltage is $6\,\text{V}$.
3. In that case, the current through the resistor would be $I = \frac{V}{R} = \frac{6}{15} = 0.4\,\text{A}.$

So a voltage drop of $6\,\text{V}$ is consistent with a current of $0.4\,\text{A}$ through the $15\,\Omega$ resistor.

But strictly speaking, because the figure is missing, a full independent derivation is not possible.