We know that, equation of a plane passing through 3 points,
$\left|\begin{array}{ccc}\mathit{x}-{\mathit{x}}_1& \mathit{y}-{\mathit{y}}_1& \mathit{z}-{\mathit{z}}_1\\ {\mathit{x}}_2-{\mathit{x}}_1& {\mathit{y}}_2-{\mathit{y}}_1& {\mathit{z}}_2-{\mathit{z}}_1\\ {\mathit{x}}_3-{\mathit{x}}_1& {\mathit{y}}_3-{\mathit{y}}_1& {\mathit{z}}_3-{\mathit{z}}_1\end{array}\right|$ = 0
⇒ $\left|\begin{array}{ccc}\mathit{x}-3& \mathit{y}+1& \mathit{z}-2\\ 2& 3& 2\\ -4& 0& 4\end{array}\right|$ = 0
⇒ (x - 3) (12 - 0) - (y + 1) (8 + 8) + (z - 2) (0 + 12) = 0
⇒ 12x - 36 - 16y - 16 + 12z - 24 = 0
⇒ 12x - 16y + 12z - 76 = 0
⇒ 3x - 4y + 3z - 19 = 0
Also ,perpendicular distance of P(6, 5, 9) to the plane 3x - 4y + 3z - 19 = 0
= $\frac{\left|3\times 6-4\times 5+3\times 9-19\right|}{\sqrt{9+16+9}}$
= $\frac{6}{\sqrt{34}}$ units