Help With Steps Of Finding Orthocenter

Question

I'm trying to find the orthocenter of $M(-8,0)$, $N(0,0)$, $P(-4,6)$.

I thought I did all of the steps right but I keep getting an answer of $(-4,6)$, but my book says $(-4,2.6667)$.

Here are the 3 steps I did.
Could someone tell me what I did wrong or show me the correct steps in finding the orthocenter?

Step 1: Find equation of line containing altitude from P to MN
$x=-4$

Step 2: Find the equation of the line containing altitude from M to PN.
Slope of PN = $\displaystyle -\frac{3}{2}$
Equation: $\displaystyle Y = \frac{3}{2}x + 12$

Step 3: Solve the system $\displaystyle Y = \frac{3}{2}(-4) + 12 = 6$

Answer 1

If a given line has slope $m$, then a perpendicular line will have slope $\frac{-1}m$. Your mistake is that you used $-m$ instead of $\frac{-1}m$, so your equation for the altitude from $M$ to $PN$ should look like $y = \frac23x + b$.