Great question! 

As you know that 2^12 gives you 1 mod 13, we are looking for the first time ever that 2^x becomes 1 mod 13.

Now, think about it this way. 2^12=1 means that 2^6 could have been 1. Or, 2^4 could have been 1, previous to 2^12. In other words, we just have to look at divisors of 2^12 first to see whether 2^x =1 is true for smaller values of x than 12.

If you see 2^5, however you try to make 2^12 with 2^5, we cannot make it happen. 

If you have further questions, let me know ASAP! Yay!