The ratio in which the line joining $(2,-4,3)$ and $(-4,5,-6)$ is divided by the plane $3x+2y+z-4=0$

A line passes through the point $(2,-4,3)$ and  $(-4,5,-6)$
The equation of the line can be written as  $t=\frac{x-2}{-4-2}=\frac{y+2}{5+4}=\frac{z-3}{-6-3}$
$x=-6t+2,y=9t-4,z=-9t+3$            
Sub this in eq of the plane $3x+2y+z-4=0$ 
$$\begin{gathered} =-18t+6+18t-8-9t+3-4=0 \\ t=\frac{-1}{3} \end{gathered}$$                            
Required point is  $(4,-2,6)$
 Required ratio is $x_1-x:x-x_2$
$$\begin{gathered} =2-4:4+4 \\ =-2:8 \\ =-1:4 \end{gathered}$$