1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -4]$ by using the line segment connecting the points where $x = -6$ and $x = -4$. 2. **Recall the formula for average rate of change:** $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ where $a = -6$ and $b = -4$. 3. **Identify the function values at the endpoints:** From the graph, $f(-6) = 20$ and $f(-4) = 0$. 4. **Calculate the average rate of change:** $$\frac{f(-4) - f(-6)}{-4 - (-6)} = \frac{0 - 20}{-4 + 6} = \frac{-20}{2}$$ 5. **Simplify the fraction:** $$\frac{-20}{2} = -10$$ 6. **Interpretation:** The average rate of change of $f(x)$ on the interval $[-6, -4]$ is $-10$. This means the function decreases by 10 units on average for each 1 unit increase in $x$ over this interval. **Final answer:** $$\boxed{-10}$$