#### Answer

Neither parallel nor perpendicular.

#### Work Step by Step

We know that two parallel lines have the same slope ($m_1=m_2$).
We also know that perpendicular lines have negative reciprocal slopes ($m_1=-\frac{1}{m_2}$).
A line in slope-intercept form has the equation:
$y=mx+b$ ($m=slope$, $b=y-intercept$)
We put the line equations into slope-intercept form:
$4x-3y=6$
$-3y=6-4x$
$y=(6-4x)/-3$
$y=-2+\frac{4}{3}x$
$y=\frac{4}{3}x-2$
$3x-4y=2$
$-4y=2-3x$
$y=(2-3x)/-4$
$y=-\frac{1}{2}+\frac{3}{4}x$
$y=\frac{3}{4}x-\frac{1}{2}$
The two slopes ($\displaystyle \frac{3}{4}$ and $\displaystyle \frac{4}{3}$) are reciprocals of each other, but they are not negative reciprocals. Thus the lines are neither parallel nor perpendicular.