We are given the system of equations:

1. $4x + 2y = -12$
2. $-2x + y = 6$

To solve this system by substitution, we will first solve one equation for one variable and then substitute that into the other equation. Let's solve the second equation for $y$:

$-2x + y = 6$

Solving for $y$:

$y = 2x + 6$

Now, substitute this expression for $y$ into the first equation:

$4x + 2(2x + 6) = -12$

Simplify and solve for $x$:

$4x + 4x + 12 = -12$ $8x + 12 = -12$ $8x = -12 - 12$ $8x = -24$ $x = -3$

Now that we have $x = -3$, substitute it back into the equation $y = 2x + 6$ to find $y$:

$y = 2(-3) + 6$ $y = -6 + 6$ $y = 0$

So, the solution to the system of equations is $x = -3$ and $y = 0$.

Let me know if you need further clarification or details!

Here are 5 related questions to expand your understanding:

1. How would you solve the system using the elimination method instead of substitution?
2. What happens if both equations represent the same line? How do you recognize that?
3. Can you graph these two lines and confirm the solution visually?
4. How would you check if a point is a solution to a given system of equations?
5. What if the system had no solution? What would that look like algebraically?

Tip: When solving by substitution, it's often easiest to solve for the variable with a coefficient of 1, like we did with $y$ in the second equation.