There are six sliders on each face.
Each slider has to be in one of three positions to release it's corresponding pin on the inner box.
Hence: 3 x 3 x 3 x 3 x 3 x 3 = 2187 combinations of slider positions on ONE face.
Therefore total number of combinations: 2187 x 2187 x 2187 x 2187.
Since my calculator wouldn't go high enough, I did it roughly on paper, using 2000 instead of 2187.
I got, if I remember, 32 followed by fifteen noughts.
If you're thinking of making this box, you MUST write down the solution...
I keep my box in the open position, in case I lose my solution.