The angle between the lines 2x = 3y = -z and 6x = -y = -4z, is

The equations of the given lines can be written in the from

$\frac{x}{3}=\frac{y}{2}=\frac{z}{-6}$ and $\frac{x}{1}=\frac{y}{-6}=\frac{z}{-3/2}$

Clearly, $3×1+2×(-6)-6×(-\frac{3}{2})=0$

So, given lines are perpendicular to each other.