To simplify the expression, first divide 8b by 2b, which equals 4. Then, simplify the expression inside the parentheses:

(a + 4) - (3a^2/b^2) * (b/6a)

Next, simplify the expression in the second set of parentheses by cancelling out terms:

(a + 4) - (3a/b) * (1/6)

Now, multiply 3a and 1 to get 3a, then multiply 6 and 1 to get 6:

(a + 4) - (3a/6)

Now divide 3a by 6 to get 1/2:

(a + 4) - (a/2)

To combine the terms, find a common denominator. Multiply 4 by 2 to get 8:

(2a + 8 - a)/2

Now, combine the like terms:

a + 8/2

Therefore, the simplified expression is:

a + 4