Avg rate of change is given by change in f(x) over change in x, in other words:
[tex]\displaystyle \frac{f(x_2)-f(x_1)}{x_2-x_1}, x_2 > x_1[/tex]
Substituting the function and your values of x gives:
[tex]\displaystyle \frac{f(3)-f(-5)}{3-(-5)} = \frac{(-3(3)^2+4(3))-(-3(-5)^2+4(-5))}{8} = \frac{-15+95}{8} \\
= \frac{80}{8} = \boxed{10}[/tex]
