I can definitely say there exist no such positive even integers, Whose sum is 0,
If you think negative integers are also classified as even and odd, Then the solution is,
Let three consecutive even integers be
X-2, X, X+2,
according to data, their sum is 0,
(X-2) + (X) + (X+2) = 0,
3X = 0,
X = 0,
Now the three integers are -2, 0, +2 !!