1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -3]$. 2. **Formula:** The average rate of change of a function $f(x)$ over an interval $[a, b]$ is given by $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ 3. **Identify values:** From the graph, we have $$a = -6, \quad f(a) = 10$$ $$b = -3, \quad f(b) = -10$$ 4. **Calculate:** Substitute these values into the formula: $$\frac{f(-3) - f(-6)}{-3 - (-6)} = \frac{-10 - 10}{-3 + 6} = \frac{-20}{3}$$ 5. **Simplify:** The fraction is already in simplest form, so the average rate of change is $$\boxed{-\frac{20}{3}}$$ This means the function decreases on average by $\frac{20}{3}$ units for each unit increase in $x$ over the interval $[-6, -3]$.