Expand the numerator: x^2+x-6 and find its derivative: 2x+1; and the denominator: x^2+3x+2 and its derivative: 2x+3.
Let u=x^2+x-6, u'=2x+1; let v=x^2+3x+2, v'=2x+3.
y'=(vu'-uv')/v^2=((x^2+3x+2)(2x+1)-(x^2+x-6)(2x+3))/(x^2+3x+2)^2.
y'=(2x^3+7x^2+7x+2-2x^3-5x^2+9x+18)/((x+1)(x+2))^2.
y'=(2x^2+16x+20)/((x+1)(x+2))^2=2(x^2+8x+10)/((x+1)(x+2))^2.