The expression to evaluate is:

$\frac{-b - c^2}{2a}$

We are given the values $a = 2$, $b = 2$, and $c = 4$. Now, let's substitute these values into the expression and simplify.

$\frac{-2 - 4^2}{2 \times 2}$

First, calculate $4^2$:

$4^2 = 16$

Now substitute this back into the expression:

$\frac{-2 - 16}{2 \times 2} = \frac{-18}{4}$

Simplify the fraction:

$\frac{-18}{4} = -\frac{9}{2}$

The final answer is:

$-\frac{9}{2}$

Would you like more details or have any questions?

Here are 5 related questions you can explore:

1. How can you simplify complex fractions step-by-step?
2. What are the properties of exponents and how do they apply here?
3. How do you convert improper fractions to mixed numbers?
4. How does substituting variables into algebraic expressions work?
5. How can you factor expressions to simplify calculations?

Tip: Always simplify the numerator and denominator separately before dividing or reducing the fraction.