Explanation

The geometric mean of two numbers is √(xy), so √(xy) = 6 gives xy = 36 on squaring. The geometric mean of three numbers is ∛(xyz), so ∛(xyz) = 6 gives xyz = 216 on cubing. Dividing the second equation by the first isolates z: z = 216/36 = 6. Note that z must equal the common geometric mean here — that is why the distractors 12, √(6) and ∛(6) cannot work. Hence option (C) 6.