What is the solution to the system of equation?

Both equations are set equal to y.  Set them equal to each other now:

y = -2x - 4

y = 2x + 4

-2x - 4 = 2x + 4

Now we solve by isolating x.  Subtract 2x from both sides:

-2x - 4 = 2x + 4

-4x - 4 = 4

And add 4 to both sides:

-4x - 4 = 4

-4x = 8

Now divide both sides by -4:

-4x = 8

x = -2

Now we substitute x into one of the original equations and simplify:

y = 2x + 4

y = 2(-2) + 4

y = -4 + 4

y = 0

So our solution:

(-2, 0)