Explanation

Put t = 2^{1/3}; then x − 2 = t + t². Cubing: (x−2)³ = t³(1+t)³ = 2(1+t)³ = 2(3 + 3t + 3t²) = 6 + 6(x−2) = 6x − 6. Thus x³ − 6x² + 12x − 8 = 6x − 6, giving x³ − 6x² + 6x = 2: option B.