Combinatorics problem with negative possibilities I know how to solve the basic number of solutions equations, such as "find the number of positive integer solutions to $x_1 + x_2 + x_3$ = 12, with ". But I have no clue how to do this problem:
Find the number of solutions of $x_1+x_2-x_3-x_4 = 0$ in integers between -4 and 4, inclusive.
If I try and solve it like the basic equations, I get $C(n+r-1,r)$$ = C(0+9-1,9)$$ = C(8,9)$, which is obviously improper. Can someone point me in the right direction on how to solve this type of problem?

Hints: (1). Let $y_1=x_1$, $y_2=x_2$, $y_3=-x_3$, $y_4=-x_4$. We want to solve $y_1+y_2+y_3+y_4=0$, with the $y_i\dots$. 
(2) Let $z_i=y_i+4$. We want to solve $z_1+z_2+z_3+z_4=\dots$. 
