Question 461564
The first statement implies N and M are congruent to 2 modulo 4. Hence,
N + M ≡ 2 + 2 ≡ 4 ≡ 0 (mod 4), so the remainder is 0.



If you do not know modular arithmetic, you could let N = 4x + 2 and M = 4y + 2, where x and y are integers. Then,
N + M = (4x + 2) + (4y + 2) = 4x + 4y + 4 = 4(x + y + 1)


This is a multiple of 4, so the remainder upon dividing by 4 is 0.


Either way works, it is just a matter of which solution you are most comfortable with. I personally prefer the first solution since it is faster and requires no algebra.