$xy -2y + 3x -6 =3$
$⇔(xy-2y)+(3x-6)=3$
$⇔y(x-2)+3(x-2)=3$
$⇔(x-2)(y+3)=3=1.3=3.1=(-1)(-3=(-3)(-1)$
+)(x-2)(y+3)=1.3
⇔$\left \{ {{x-2=1} \atop {y+3=3}} \right.$
⇔$\left \{ {{x=3} \atop {y=0}} \right.$
+)(x-2)(y+3)=3.1
⇔$\left \{ {{x-2=3} \atop {y+3=1}} \right.$
⇔$\left \{ {{x=5} \atop {y=-2}} \right.$
+)(x-2)(y+3)=(-1)(-3)
⇔$\left \{ {{x-2=-1} \atop {y+3=-3}} \right.$
⇔$\left \{ {{x=1} \atop {y=-6}} \right.$
+)(x-2)(y+3)=(-3)(-1)
⇔$\left \{ {{x-2=-3} \atop {y+3=-1}} \right.$
⇔$\left \{ {{x=-1} \atop {y=-4}} \right.$
