Explanation

Let t = cube-root(2), so t^3 = 2 and x - 2 = t + t^2. Cubing: (x-2)^3 = (t+t^2)^3 = t^3 + 3t^4 + 3t^5 + t^6 = 2 + 6t + 6t^2 + 4 = 6 + 6(x-2) = 6x - 6. Expanding (x-2)^3 = x^3 - 6x^2 + 12x - 8 and equating to 6x - 6 gives x^3 - 6x^2 + 6x = 2. Hence option A.