Your table of values is so difficult to read that many of us helpers would just skip your post.
x f(x) -6 2.5 -2 2.5 0 2 2 0 3 5 5 2.5 1 0.5 could be put into far clearer format as follows:
x f(x)
-- -----
-6 2.5
-2 2.5
and so on. Please fix it.
The "average rate of change" formula is
f(x2) - f(x1)
av r of c = ---------------
x2-x1
so if you go from (-6, 2.5) to (2.5, 10.5), the av r of c would be
10.5 - 2.5 9 18
------------------ = -------- = -----
2.5-(-6) 8.5 17
This may or may not be your final answer. Again, please put your data table into readable form and then find the av r of c over the interval [-2,3].