1. **State the problem:** We need to find the value of the piecewise function $f(x)$ at $x = -6$. 2. **Recall the piecewise definition:** $$ f(x) = \begin{cases} -x + 4 & \text{if } x \leq -2 \\ 8x + 5 & \text{if } -2 < x \leq 4 \\ -3x - 1 & \text{if } x > 4 \end{cases} $$ 3. **Determine which piece applies:** Since $-6 \leq -2$, we use the first piece: $f(x) = -x + 4$. 4. **Substitute $x = -6$ into the first piece:** $$ f(-6) = -(-6) + 4 = 6 + 4 = 10 $$ 5. **Final answer:** $$ f(-6) = 10 $$ This means the function value at $x = -6$ is 10.