To figure out whether lines are parallel or perpendicular you have to look at their slopes. If they are the same that means the lines are parallel. If opposite signs and the inverse of each other, they are perpendicular.

x + 4/3y = 2

4/3y = 2 - x

y= 3/4(2- x)

y = 1.5 - 3/4x

m = slope = -3/4

3x + 4y = 12

4y = 12 - 3x

y = 3 - 3/4x

m = -3/4

The lines have the same slopes and different y intercepts, thus the lines are parallel.