B

Step 1: Understand mutual inductance.
Mutual inductance ($M$) between two coils is given by the formula:
$$M = k \sqrt{L_1 L_2}$$
where $k$ is the coupling coefficient (ranging from 0 to 1), and $L_1$ and $L_2$ are the self-inductances of the coils.

Step 2: Analyze factors affecting mutual inductance.
The mutual inductance can be increased by:

• Increasing the number of turns: This increases the self-inductance of each coil ($L_1$, $L_2$), thereby increasing $M$ since $M$ is proportional to the square root of the product of self-inductances.
• Using a core material with high magnetic permeability: While it’s not mentioned in the options, using a ferromagnetic core increases mutual inductance, but the core option provided (wood) would not help.

Step 3: Evaluate the options.
- Option A: Decreasing the number of turns decreases mutual inductance.
- Option B: Increasing the number of turns will increase mutual inductance.
- Option C: Winding on a wooden core does not enhance magnetic coupling.
- Option D: Not applicable as Option B stands.

Conclusion: The correct answer is Option B: Increasing the number of turns in the coils.