The interior of a rectangular carton has a ratio of length to width to height of 3:2:2.
Let 3k = the length of the carton
Let 2k = the width of the carton
Let 2k = the height of the carton

Note: Our goal is to find an equivalent value to 2k (the height of the carton)

Note: This guarantees that the ratio of length to width to height of 3:2:2

The carton's volume is x.
Volume of carton = (length)(width)(height)
So, we can write: (3k)(2k)(2k) = x
Simplify: \(12k^3 = x\)
Divide both sides by 12 to get: \(k^3 = \frac{x}{12}\)
Take the cube root of both sides to get: \(k = \sqrt[3]{\frac{x}{12}}\)
Multiply both sides of the equation by 2 to get: \(2k = 2\sqrt[3]{\frac{x}{12}}\)

Check the answer choices.....\(2\sqrt[3]{\frac{x}{12}}\) is not among them.
So it looks like we need to find an equivalent way to express \(2\sqrt[3]{\frac{x}{12}}\)
Since \(2= \sqrt[3]{8}\), we can write: \(2\sqrt[3]{\frac{x}{12}} = (\sqrt[3]{8})(\sqrt[3]{\frac{x}{12}})= \sqrt[3]{\frac{8x}{12}}= \sqrt[3]{\frac{2x}{3}}\)

Answer: B