Explanation:

- Mean Proportional:

- It is the square root of the product of two numbers.

- Between 8.1 and 3.6, it is v(8.1 * 3.6) = v29.16 = 5.4.

- Third Proportional:

- If a : b = b : c, then c is the third proportional.

- For 2 and 3, (2 * 3) / 2 = 4.5.

- Calculation of the Ratio:

- Mean proportional is 5.4.

- Third proportional is 4.5.

- Ratio is 5.4 : 4.5.

- Simplified, it is 6 : 5.

- Option Analysis:

- Option 1 (6 : 5) is the correct ratio.

- Option 2, 3, 4 are incorrect as they present different ratios.

Correct Answer: Option 1, 6 : 5