I've seen in other puzzle games they have a preview of each action, so you can at least immediately see what will happen to a die if you move it up/down/left/right
As for the die in top right corner, well, try making a smooth 90 degree animation when you rotate it in each direction.
But i will be honest, i haven't seen this mechanic work well in other games too, it always seems confusing to me, but maybe that's just me.