To simplify the expression:

Expand the numerator:
(a-3y)^2 = a^2 - 6ay + 9y^2
(a^2 - 6ay + 9y^2)/12y = (a^2/12y) - (6ay/12y) + (9y^2/12y)
= (a^2/12y) - (1/2)a + (3/4)y

Expand the denominator:
9y^2 - a^2 = (3y - a)(3y + a)
(3y-a)(3y+a)/16x = ((3y-a)/16x)((3y+a)/16x)
= (3y-a)(3y+a)/256x^2
= (9y^2 - a^2)/256x^2
= (9y^2/256x^2) - (a^2/256x^2)
= (9y^2/256x^2) - (1/256)(a^2/x^2)

So the simplified expression is:
((a^2/12y) - (1/2)a + (3/4)y) / ((9y^2/256x^2) - (1/256)(a^2/x^2))