Solution:
(a) The length of perpendicular from the point $(2,3,-5)$ on the plane $x+2 y-2 z=9 \Rightarrow x+2 y-2 z-9=0$ is
$\frac{\left|a x_{1}+b y_{1}+c z_{1}+d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}}$
$=\frac{|2(1)+2(3)-2(-5)-9|}{\sqrt{(1)^{2}+(2)^{2}+(-2)^{2}}}$
$=\frac{|9|}{\sqrt{1+4+4}}=\frac{9}{\sqrt{9}}=\frac{9}{3}=3$
(b) The length of perpendicular from the point $(-6,0,0)$ on the plane $2 x-3 y+6 z-2=0$ is
$\frac{\left|a x_{1}+b y_{1}+c z_{1}+d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}}$
$\begin{aligned}
\frac{|2(-6)-3(0)+6(0)-2|}{\sqrt{(2)^{2}+(-3)^{2}+(6)^{2}}} \\
= \frac{|-14|}{\sqrt{4+9+36}}=\frac{14}{\sqrt{49}}=\frac{14}{7}=2
\end{aligned}$