In order to find the solution (point of intersection) of two lines, you must solve them simultaneously for the x-coordinates and y-coordinates.
Let -4x - 2y = -12 be (eq1)
& 2x + 4y = -12 be (eq2)
Now you have to find a way to multiply one or two of the equations so that upon adding or subtracting them, the two equations will become a single equation with one solvable variable.
by multiplying (eq 1) by 2
2(-4x - 2y = -12)
Now let -8x - 4y = -24 (eq1ᵃ)
So, -8x - 4y + (2x + 4y) = -24 + (-12) [eq1ᵃ + eq2]
⇒ -8x + 2x - 4y + 4y = - 36
- 6x = - 36
⇒ x = 6
By substituting x = 6 into eq2
⇒ 2(6) + 4y = - 12
12 + 4y = - 12
4y = - 24
⇒ y = -6
Thus the solution set is (6 , -6)