Question 1014940
Let n = 1st odd integer
then n+2 = 2nd odd integer
n+4 = 3rd odd integer
and n+6 = 4th odd integer
 
Hence n + (n+2) + (n+4) + (n+6) = -268
from this we get

4n+ 12 = -268, or 4n = -280, or n = -70.

This would imply that the four consecutive ODD integers are -70, -68, -66, -64.  Contradiction.  

Therefore there's no solution to this problem.