Hi
two lines are parallel only if they have the same slope.
So : 3x+4y = 12
4y = 12 -3x
y = 12/4 - 3x/4
y = 3 - 3/4 X
y = -3/4 X +3
Slope is -3/4
and 6x+2y = 6
2y = 6 -6x
y = 6/2 - 6x/2
y = 3 - 3X
y = -3X +3
Slope is = -3
As -3/4 ≠ -3 then the two lines are not parallel.