3x + 4y = -2
x-6y = -8
3 x -6 + 4 x 1 = -2
-2 - 6 x 1 = -8
are you guessing at the answers in the last two lines?
take the first equation and multiply it by 3 to get
9x + 12y = -6
take the second equation multiply it by 2 to get
2x - 12y = -16
add them
11x = -22
x = -2
sub that back into the first ...
3(-2) + 4y = -2
-6 + 4y = -2
4y = 4
y = 1
so x=-2, y = 1
(they work in both original equations)