Question: Given $f(x) = -2(x - 3)(x + 4)$, find $f(6)$.
1. **State the problem:** We need to find the value of the function $f(x) = -2(x - 3)(x + 4)$ when $x = 6$.
2. **Formula used:** The function is given as $f(x) = -2(x - 3)(x + 4)$.
3. **Substitute $x = 6$ into the function:**
$$f(6) = -2(6 - 3)(6 + 4)$$
4. **Simplify inside the parentheses:**
$$f(6) = -2(3)(10)$$
5. **Multiply the terms:**
$$f(6) = -2 \times 3 \times 10$$
6. **Calculate step-by-step:**
$$f(6) = -6 \times 10$$
$$f(6) = -60$$
7. **Final answer:**
$$\boxed{-60}$$
So, the value of $f(6)$ is $-60$.