Did you mean y+x=6 and y-x=6?
To draw linear graphs the easiest way is to draw a line through the intercepts, which are easy to find.
Take y+x=6. Put x=0 and that means y=6, which is the y-intercept, so mark 6 on the y axis. Now put y=0, which makes x=6, so mark 6, the x-intercept, on the x axis. Draw a line through the points you just marked on the axes. That gives you the line y+x=6.
Now take the other equation, y-x=6. When x=0, y=6, which is already marked.
Now put y=0, which leaves -x=6, or x=-6 so mark -6 on the x axis. Draw a line through this point and 6 on the y axis. So now you have two lines intersecting at y=6 and x=0, which is the point (0,6).
(Note that y+y=6 is a horizontal line (y=3), that is, parallel to the x axis, it cuts the y axis at 3. So if you really did mean y+y=6, this horizontal line will intersect y-x=6 at (-3,3).)