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

(6a / (a²-b²) - 2 / (a+b) + 3 / (b-a)) = ((6a(a+b) - 2(a²-b²) + 3(a²-b²)) / (a²-b²)(a+b)(b-a))

Next, simplify the numerator:

= ((6a² + 6ab - 2a² + 2b² + 3a² - 3b²) / (a²-b²)(a+b)(b-a))
= ((7a² + 6ab - b²) / (a² - b²)(a + b)(b - a))

Now, we want to divide this expression by (4a + 4b):

= (7a² + 6ab - b²) / ((a² - b²)(a + b)(b - a)) ÷ (4a + 4b)
= (7a² + 6ab - b²) / ((a - b)(a + b)(a + b)(-(a + b))) ÷ 4(a + b)
= (7a² + 6ab - b²) / ((a - b)(a + b)(-a - b)) ÷ 4(a + b)
= (7a² + 6ab - b²) / (- (a^2 - b^2) (a + b)) ÷ 4(a + b)

Now, we can simplify further if needed.