Find p such that the lines whose equations are 3px + 8y = 5 and 6y - 4px = -1 are perpendicular.
The answer should be p = 2, -2
But I don't understand how to obtain that.
Right the equations in y=mx+b form. In the first equation you'll have the slope $\displaystyle m_1=\frac{-3p}{8}$ and in the second $\displaystyle m_2=\frac{4p}{6}=\frac{2p}{3}$. Use what you know about the relationship between the slopes of perpendicular lines to solve for p.