Assuming the parent function is csc(x), it consists of U-shaped curves (upright or inverted) with asymptotes at regular intervals which are for x equal to multiples of π. For odd multiples of π/2, we have vertices at y=1 and y=-1 for upright and inverted curves respectively. csc(x) is not symmetrical about the y axis.
The transformation for csc(x⁶) is to make the U curves very narrow so that the asymptotes are much close together. The vertices are still at y=1 and -1, but, like the asymptotes, are closer together. Unlike the parent function, csc(x⁶) is reflected in the y axis, so is symmetrical about the y axis. Like the parent function, the curves alternate between upright and inverted.