The slope of line [tex]m[/tex] is [tex]\frac{-3-1}{2-6}=1[/tex], so its equation is
[tex]y-1=x-6\implies y=x-5[/tex]
The slope of line [tex]n[/tex] is [tex]\frac{-6-3}{5-2}=-3[/tex], so its equation is
[tex]y-3=-3(x-2)\implies y=-3x+9[/tex]
The two lines intersect wherever the two equations are the same:
[tex]x-5=-3x+9\implies4x=14\implies x=\dfrac72\implies y=-\frac32[/tex]
The point of intersection is then [tex]\left(\frac72,-\frac32\right)[/tex].
