To simplify this expression, we first need to find a common denominator for the fractions in the numerator.

Let's rewrite the expression:
(4a/3b/2 - 12a/2b/3) / (2ab)

First, let's simplify the fractions in the numerator:

4a/3b = (4a/3) / b = 4a/3b
12a/2b = (12a/2) / b = 6a/b

Now, rewrite the expression with the simplified fractions:
(4a/3b - 6a/b) / (2ab)

Now, find a common denominator for the fractions in the numerator:
To find a common denominator for 3b and b, we multiply them together to get 3b^2.

(4a/3b)(b/b) = 4ab/3b^2
(6a/b)(3/3) = 18a/3b^2

Now, rewrite the expression with the common denominator:
(4ab/3b^2 - 18a/3b^2) / 2ab

Now, subtract the fractions in the numerator:
(4ab - 18a) / 3b^2 / 2ab

Now the expression is:
(4ab - 18a) / 3b^2 / 2ab

To simplify further, we need to divide the numerator by the denominator:
(4ab - 18a) / (3b^2 * 2ab)
(4ab - 18a) / 6ab^3

Thus, the final simplified expression is:
(4ab - 18a) / 6ab^3