First part:
(3x+2y)/(x-y)÷(9x²+12xy+4y²)=(3x+2y)/((x-y)(9x²+12xy+4y²))=
(3x+2y)/((x-y)(3x+2y)²)=1/((x-y)(3x+2y));
Now take this result and divide by 4y²/(x²-y²) which is the same as multiplying by (x²-y²)/4y²:
(1/((x-y)(3x+2y)))((x²-y²)/4y²)=
(1/((x-y)(3x+2y)))(x-y)(x+y)/4y²=
(x+y)/(4y²(3x+2y)).