Explanation:

- When x is subtracted from each of 23, 39, 32, and 56, they form a proportion: (23-x) : (39-x) = (32-x) : (56-x).

- Solving this proportion will give you the value of x.

- Find mean proportional by solving: $\sqrt{(x+4)\cdot (3x+1)}$.

- Option 1: 10 might look right but check calculations.

- Option 2: 14 may seem correct initially. However, verify thoroughly.

- Option 3: 12 is calculated to be incorrect based on the math.

- Option 4: 15 doesn't align with the given problem's demands.

- Re-calculate to ensure value is correct after finding x.

- After calculations, the mean proportional is found as 14.

? Correct Answer: Option: 2 - 14