#### Answer

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:
$4x-3y=8$
$-3y=8-4x$
$y=-8/3+4/3x$
$y=4/3x-8/3$
And:
$4y+3x=12$
$4y=-3x+12$
$y=-3/4x+3$
The two slopes ($4/3$ and $-3/4$) are negative reciprocals. Thus the lines are perpendicular.