Establish a list of 4^N to see the cycle: 4,16,64,256,1024...
So when N is even, the last digit is always 6 and when N is odd, the last digit is 4.
We can rephrase as: Is N even or odd?

1) N^2 is divisible by 4 means N has at least one factor of 2, so Sufficient.
2) N+2 is divisible by 6 means that N is a multiple of 6, minus 2.
Since every multiple of 6 is even and since an even number -2 is always even as well, 2) is Sufficient.

yeah...We can rephrase as: Is N even or odd?

i.e.
4^N where N is even is alway gonna end in 6
4^N where N is odd is alway gonna end in 4