We are given the equation:

$-4x = -2y + 6$

Let's solve for $y$ in terms of $x$:

Step 1: Isolate the $-2y$ term

Add $2y$ to both sides of the equation:

$-4x + 2y = 6$

Step 2: Isolate the $2y$ term

To solve for $y$, we want to isolate the $y$ term. Subtract $-4x$ from both sides:

$2y = 4x + 6$

Step 3: Solve for $y$

Now, divide both sides by 2 to isolate $y$:

$y = \frac{4x + 6}{2}$

Simplify the expression:

$y = 2x + 3$

The equation is now solved for $y$ in terms of $x$:

$y = 2x + 3$

Would you like further details or clarifications on any steps?

Here are 5 related questions to expand on this problem:

1. What is the slope of the line represented by $y = 2x + 3$?
2. How do we graph the equation $y = 2x + 3$?
3. Can you find the x-intercept and y-intercept of this equation?
4. What would the equation look like if the slope were different, say $y = 5x + 3$?
5. How do we find the point of intersection of $y = 2x + 3$ with another line?

Tip: When solving linear equations, try to get one variable isolated step by step for clarity and simplicity.