We have
$4 x y+2 x+6 y+3=0$
$\Rightarrow 2 x(2 y+1)+3(2 y+1)=0$
$\Rightarrow (2 x+3)(2 y+1)=0$
Equation of lines are $x=\frac{-3}{2}$ and $y=-\frac{1}{2}$
Equations of line passing through $(2,1)$ and
perpendicular to the line $x=\frac{23}{2}$ and $y=\frac{1}{2}$ are
$y-1=0 \text { and } x-2=0$
$\therefore $ Combining equation of lines are
$(y-1)(x-2)=0$
$\Rightarrow x y-x-2 y+2=0$