To find the y-coordinate of the y-intercept of a polynomial function, we need to evaluate the function $f(x)$ at $x = 0$.

The given polynomial function is:

$f(x) = -2(x + 4)(x + 1)(x - 2)$

Now, substitute $x = 0$ into the equation to find the y-intercept:

$f(0) = -2(0 + 4)(0 + 1)(0 - 2)$

Simplifying:

$f(0) = -2(4)(1)(-2)$

$f(0) = -2(4)(-2) = -2 \times -8 = 16$

Thus, the y-coordinate of the y-intercept is 16.

Would you like more details or have any other questions? Here are some related questions:

1. How do you find the roots of this polynomial function?
2. What is the degree of this polynomial function?
3. How do you determine whether the function opens upward or downward?
4. How would the graph of this function look based on its intercepts and roots?
5. What is the leading term of the polynomial when fully expanded?

Tip: The y-intercept of a function is always found by substituting $x = 0$ in the equation, regardless of the type of function.