To solve the equation \(-6x - 12y = -24\), you can first simplify it by dividing through by \(-6\), which is the greatest common divisor of all the coefficients.

\[
\frac{-6x - 12y}{-6} = \frac{-24}{-6}
\]

This simplifies to:

\[
x + 2y = 4
\]

### Solution:
The simplified equation is \(x + 2y = 4\).

- If you want to solve for \(x\) in terms of \(y\), rearrange it:
  \[
  x = 4 - 2y
  \]
  This gives the solution for \(x\) in terms of \(y\).

- If you want to solve for \(y\) in terms of \(x\), rearrange it:
  \[
  2y = 4 - x
  \]
  \[
  y = \frac{4 - x}{2}
  \]
  This gives the solution for \(y\) in terms of \(x\).

Would you like to proceed with graphing or finding specific values?

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Here are five related questions:

1. How would you graph \(x + 2y = 4\)?
2. What is the slope of the line \(x + 2y = 4\)?
3. How would you solve the system of equations \(x + 2y = 4\) and \(x - y = 1\)?
4. What are the intercepts of the line \(x + 2y = 4\)?
5. Can you express \(y\) as a function of \(x\) in a more general equation?

**Tip:** When solving linear equations, try to simplify them first by dividing all terms by their greatest common factor.

Learn how to solve the linear equation -6x -12y = -24 by simplifying it step-by-step. This algebra problem covers key concepts such as simplification of linear equations and rearranging variables. Suitable for students in Grades 6-8.

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