Two lines  $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$ and $\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}$  intersect at the point R. The reflection of R in the xy-plane has coordinates :-

Point on  ${\text{L}}_1(\lambda +3,3\lambda -1,-\lambda +6)$
Point on  ${\text{L}}_2(7\mu -5,-6\mu +2,4\mu +3)$
   $\Rightarrow \lambda +3=7\mu -5$
   $3\lambda -1=-6\mu +2$        …. (1)
Point on   $(2,-4,7)$        …. (2)
   $\Rightarrow \lambda =-1,\mu =1$
Reflection is   $(2,-4,-7)$