I dont give exact answer,but i can give you approach that i follows.
Lets say we have a number n (say 13),now if i find mod of this with some number(+ve) say m=4, it will give me 1(13%4).
Now suppose i add multiple of 4(4x) into n.Say 13+(4*2),will it change my Mode?No way ,right?
Now say i have -ve number -13,now if i add multiple of 4,that is greater that 13 say 16,now it becomes -13+16,which is 3%4=3.
Hope this clears,-4mod2,will be (-4+2*3)=(-4+6)=(2)mod2,which is 0.