We are given the equation:

$-2c + 4x = -6$

To solve for $x$, follow these steps:

1. Isolate the term with $x$:

   $4x = -6 + 2c$

2. Solve for $x$ by dividing both sides by 4:

   $x = \frac{-6 + 2c}{4}$

3. Simplify the expression if possible:

   $x = \frac{-6}{4} + \frac{2c}{4}$ $x = -\frac{3}{2} + \frac{c}{2}$

Thus, the solution is:

$x = \frac{c}{2} - \frac{3}{2}$

Would you like more details or further explanation?

Here are 5 related questions you could explore:

1. How would the solution change if the equation was $-2c + 5x = -6$?
2. What if the constant on the right side was a different number, like $-10$?
3. How can you check if the solution is correct for specific values of $c$?
4. What if we had $-2c - 4x = -6$? How would the steps change?
5. How would the solution change if the coefficient of $x$ was negative?

Tip: Always simplify the expression as much as possible when solving for a variable.