Since you have a ratio of length to width to height of 3:2:2, then we can safely assume that the size of the length is 3a and the size of width = size of height = 2a. This makes the volume of the box 3a*2a*2a = 12a^3 = x. This in turn makes a = third degree root of (x/12), thus making 2a = 2*[third degree root of x/12)]. What you need to do now is to "insert" the 2 in front of the third degree root "into" the third degree root and you get that 2a or the height is [third degree root of (8x/12)]. Simplify by 4 under the third degree root and you get height = third degree root of (2x/3).

Edit: I added a photo of the thing, since I hate writing in words third degree root...

thanks!