Question 705949
The two equations are parallel lines if their slopes are equal. Meaning: if they have the same slope, they do not intersect at any point and therefore parallel to each other. 

First, change the equations to the format y=mx + b. In this equation, m is the slope.

y=2x-12; m=2

6x+3y=0 ==> 3y=-6x ==> y=-2x; m=-2

You will notice that the values of the slope are equal but different in sign. Therefore, they are two intersecting lines and are in fact perpendicular to each other.