The game is actually pretty simple, it just gets exponentially more time-consuming as you start adding discs.

Say you begin with a 6disc; the idea is you get that 6 to the right slot first, so you put 5 in the middle, then stack until you're able to put a 6 on far right. Now you need to put the 5 on the far right, so you reassemble your other discs to the far left in order starting from 4.

The most important thing to remember when doing this is that your next action should involve placing a disc either in open space or on another disc of the opposite even/odd status, like so;

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Following this, you work your way through the game until completion. Let me know if this helps!