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Simply consider what ARE the sums of four consecutive non-negative integers: 0+1+2+3 = 6
1+2+3+4 = 10
2+3+4+5 = 14
3+4+5+6 = 18
.... You can see that it's any number of the form: 6 plus a (non-negative integer) multiple of 4.
A more mathematical proof is to consider an arbitrary starting number n, then: n+(n+1)+(n+2)+(n+3) = 4*n + 6 (which is the same as concluded above).
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