(x^3+8) x ((x-2)/(x^2-2x+4))/ (x^2-4)/(x-6)

you have

(x+2)(x^2-2x+4) * (x-2)(x^2-2x+4) / (x+2)(x-2)(x-6)

(x^2-2x+4)^2 / (x-6)