Answer
The two lines are parallel when $k=-1.5 (or -3/2)$.
The two lines are perpendicular when $k = 24$.
Work Step by Step
$12y = -3x+8$ and $6y = kx -5$
$12y = -3x+8$
$12y/12 = (-3x+8)/12$
$y = -1/4*x + 2/3$
$6y = kx-5$
$6y/6 = (kx-5)/6$
$y = k/6*x - 5/6$
$y = 1/6*k*x - 5/6$
Parallel
$-1/4 = 1/6 * k$
$24*(-1/4) = 24*(1/6*k)$
$-6 = 4k$
$-6/4 = 4k/4$
$-3/2 = k$
Perpendicular
$-1/4 * (1/6 * k) = -1$
$-1/24 * k = -1$
$-24 * -1/24 * k = -1 * -24$
$k = 24$
$y = 1/6 * k * x -5/6$
$y = 1/6 * 24 *x-5/6$
$y = 4x-5/6$
