# Discrete signal testing for periodicity

How would one go about determining if the following discrete time signal x[n] is periodic, and if it is, determine its fundamental period?

I understand that the period for the second exponential term is 6, but apart from that I am unable to further my calculation.

The answer to the question above is:

but I fail to understand how the equation highlighted in yellow comes to be. Any help with this matter would be appreciated.