Let required plane is (using concept of family of plane)

$x+y+z-1+t\left(2x+3y-z+4\right)=0$

$\Rightarrow \left(1+2t\right)x+\left(1+3t\right)y+\left(1-t\right)z-1+4t=0$

Again $DR$ of $y-$ axis is $\left(0,1,0\right)$

Since plane is parallel to $y-$ axis

Hence $\left(1+2t\right)\times 0+\left(1+3t\right)\times 1+\left(1-t\right)\times 0=0$

$\Rightarrow t=-\frac{1}{3}$

$\therefore$ required plane is $\frac{1}{3}x+\frac{4}{3}z-\frac{7}{3}=0$

$\Rightarrow x+4z-7=0$

Which satisfy $\left(3,2,1\right)$