1. The problem asks to find $f(10)$ for the piecewise function defined as: $$f(x) = \begin{cases} -\frac{x}{2} + 7 & \text{if } x \leq 6 \\ x - 2 & \text{if } x > 6 \end{cases}$$ 2. Since $10 > 6$, we use the second piece of the function: $$f(10) = 10 - 2$$ 3. Calculate the value: $$f(10) = 8$$ 4. Therefore, the value of $f(10)$ is 8.