Given data:
The first set of equations are x+y=4, and x=6.
The second set of equations are 3x-y=12 and y=-6.
The point of intersection of first set of te equations is,
6+y=4
y=-2
The first point is (6, -2).
The point of intersection of second set of te equations is,
3x-(-6)=12
3x+6=12
3x=6
x=2
The second point is (2, -6).
The equation of the line passing through (6, -2) and (2, -6) is,
![\begin{gathered} y-(-2)=\frac{-6-(-2)}{2-6}(x-6) \\ y+2=\frac{-6+2}{-4}(x-6) \\ y+2=x-6 \\ y=x-8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y-%28-2%29%3D%5Cfrac%7B-6-%28-2%29%7D%7B2-6%7D%28x-6%29%20%5C%5C%20y%2B2%3D%5Cfrac%7B-6%2B2%7D%7B-4%7D%28x-6%29%20%5C%5C%20y%2B2%3Dx-6%20%5C%5C%20y%3Dx-8%20%5Cend%7Bgathered%7D)
Thus, the required equation of the line is y=x-8.