1. **Problem statement:** Given the piecewise function $$h(x) = \begin{cases} -2x + 4 & \text{if } x \leq 1 \\ x^2 + 1 & \text{if } x > 1 \end{cases}$$ Find the value of $h(-1)$. 2. **Identify which piece to use:** Since $-1 \leq 1$, we use the first piece of the function: $$h(x) = -2x + 4$$ 3. **Substitute $x = -1$ into the first piece:** $$h(-1) = -2(-1) + 4$$ 4. **Simplify the expression:** $$h(-1) = 2 + 4 = 6$$ 5. **Conclusion:** The value of $h(-1)$ is 6. **Final answer:** (A) 6