Equations of plane passing through (4,4,0) is given by a(x−4)+b(y−4)+c(z−0)=0, where a,b,c are DR's of normal to the plane.
Since this plane is ⊥ to the given plans, therefore, we get 2a+b+2c=0
and 3a+3b+2c=0
By cross-multiplication method 2−6a=4−6−b=6−3c ⇒−4a=2b=3c
So, the required equation of plane is −4(x−4)+2(y−4)+3(z)=0 ⇒−4x+16+2y−8+3z=0 ⇒4x−2y−3z=8