Simplifying Doughnut Nikhil Kotha

In example doughnut, if you stretch out the doughnut to make 1 long chain you'll see that a repeats at the start and the end to we join together same chain.

we want to make an extra extra long chain with 16 cards, but you can just repeat the original chain because of the a at the start and end.

Furthermore, 4sides with 4card/side = 16 cards total so our extra extra long chain works!

Now it is just a matter of formatting we can use the example layout. For the possibilities since there are 8 different terms(a+a and 2a are algebraically the same but say there different because question showed they are different)  so there are 8 ways.