How to solve rubix-cube like symmetric encryption
Is this the correct way to solve a rubix cube (reversing the moves)?


This isn't really a question about cryptography, and might be better suited for a math or even puzzling stackexchange site. 

That being said, while reversing the moves is a way, and is probably the way that you would use to undo the transpositions of your cipher considering you use the ordering of moves as your key, that does not necessarily mean that given an actual Rubik's cube the solution is to invert the moves that shuffled it from the initial position.


  If not, what would the correct way be?


There apparently exist optimal algorithms for solving a traditional 3x3x3 cube in 20 steps. These don't appear to assume that you are inverting the steps that shuffled the cube. Your setup may be larger, but that still doesn't bode well for using the shuffling as some kind of cryptographic hardness assumption.