Whether lines are parallel, perpendicular, or neither depends on their slopes, so let’s get them both into y=mx +b form
The first one already is in that form, and the Slope is -3
Now we just need to get the other one in that form
-2x+6y=3
ADD 2x to both sides
6y=2x+3
DIVIDE both sides by 6
Y=(2/6)x +1/2
2/6 = 1/3
The Slope for the second line is 1/3
The slopes 1/3 and -3 are perpendicular, since 1/3 inverted and made negative equals -3