Explanation:

- We start with the proportion 8 : x :: x : 32.

- This means 8/x = x/32.

- Solve the equation by cross-multiplying: 8 * 32 = x * x.

- Simplifies to 256 = x².

- Take the positive square root of both sides: x = 16.

Options:

- Option 1: 20 - Incorrect, as 20² is not 256.

- Option 2: 16 - Correct, since 16² is 256.

- Option 3: 4 - Incorrect, as 4² is 16, not 256.

- Option 4: 12 - Incorrect, since 12² is 144, not 256.