To solve the equation $2x - 4y = 8$ for $y$, we need to isolate $y$ on one side of the equation.

Step-by-Step Solution:

1. Start with the given equation: $2x - 4y = 8$

2. Subtract $2x$ from both sides to move the $x$ term to the right side: $-4y = 8 - 2x$

3. Divide every term by $-4$ to solve for $y$: $y = \frac{8 - 2x}{-4}$

4. Simplify the equation by dividing both terms in the numerator by $-4$: $y = \frac{8}{-4} - \frac{2x}{-4}$ $y = -2 + \frac{x}{2}$

5. Rearrange the equation to match the format seen in the answer choices: $y = \frac{1}{2}x - 2$

So, the correct answer is:

$\boxed{y = \frac{1}{2}x - 2}$

This matches the second option in the provided choices.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What is the process to rearrange an equation with variables on both sides?
2. How can we graph the equation $y = \frac{1}{2}x - 2$ on the coordinate plane?
3. What are the steps to solve a linear equation using the substitution method?
4. How does the slope-intercept form help in understanding linear equations?
5. What is the significance of the slope and y-intercept in the equation $y = \frac{1}{2}x - 2$?

Tip: When solving for a variable, always aim to simplify the equation step by step to avoid errors and ensure clarity.