To determine $R$, the circuit diagram is required, because power dissipation depends on how the resistor is connected and on the source values.

The question says “If in the circuit, power dissipation is $150\,\text{W}$”, but the actual circuit is not provided in the prompt. Without the circuit, we cannot uniquely calculate $R$ from the given options.

Why the circuit is necessary

Power in a resistor can be found using any of: $P = VI = I^2R = \frac{V^2}{R}$ But to use these, we must know at least one of the following from the circuit:

1. Voltage across $R$
2. Current through $R$
3. Equivalent circuit arrangement
4. Source values and other resistances

Since none of this information is visible, the value of $R$ cannot be derived uniquely from physics alone.

Comparison with stored answer

The stored correct answer is B: $6\,\Omega$.

However, because the circuit diagram is missing, I cannot verify that result from the information given.

So, I do not agree with the stored answer based solely on the provided prompt, not because $6\,\Omega$ is necessarily wrong, but because the problem statement is incomplete.

If you provide the circuit image or describe the circuit connections and source values, I can solve it fully step-by-step.