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To find the mean proportional of two numbers, we find the square root of their product. Given the numbers 8 * a^2 and 18 / a^4, let's calculate their mean proportional.

Step-by-Step Solution
Set up the formula for the mean proportional:
The mean proportional of two quantities x and y is the square root of (x * y).
Mean Proportional = Square Root of ((8 * a^2) * (18 / a^4))

Multiply the expressions inside the square root:
First, multiply the coefficients: 8 * 18 = 144.
Next, multiply the variables: a^2 * (1 / a^4) = a^2 / a^4 = 1 / a^2.
So, the product is 144 / a^2.

Take the square root:
Mean Proportional = Square Root of (144 / a^2)
Since the square root of 144 is 12 and the square root of a^2 is a, we get:
Mean Proportional = 12 / a

Correct Option
Option D: 12/a