2x - 4y = -2
2x + 3y = 12

2x - 4y = -2
2x + 3y = 12

using equation 1
2x - 4y = -2
2x = 4y -2
x = (4y - 2)/2

now plug X into equation 2
2((4y-2)/2) + 3y = 12
multiplying 2 and dividing 2 cancel out leaving us with
4y - 2 + 3y = 12
combine like terms
7y -2 = 12
add 2
7y = 14
now divide by 7
y = 2

knowing that y is equal to 2 we can plug 2 into the first equation

2x - 4(2) = -2
2x - 8 = -2
add 8
2x = 6
divide by 2
x = 3

SO y=2 and x=3