Explanation:

To find the mean proportional (or geometric mean) between two numbers, you take the square root of their product.

- Mean Proportional Calculation:

- Calculate the product of the two numbers: \(64 \times 4096 = 262144\).

- Take the square root of the product: \(\sqrt{262144} = 512\).

- Explanation for Each Option:

- Option 1 (8): This is incorrect as shown by the calculation above.

- Option 2 (512): This is correct, since the mean proportional between 64 and 4096 is 512.

- Option 3 (128): This is incorrect according to our calculation.

- Option 4 (192): This does not match the calculated result.

The correct answer is Option 2: 512.

.