problem: Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
solution: We find the slopes of the two lines and set them equal to each other, since parallel lines have the same slope. This gives $3a+2=\frac{a}{2}-2$, which implies $a=\boxed{-\frac{8}{5}}$.