To find where they intersect you need to find where they equal each other. Since you already know what y equals in terms of x from the blue equation you can plug that into the red equation to solve for x
[tex]x + 4(2x - 6) = 12 \\ x + 8x - 24 = 12 \\ 9x = 36 \\ x = 4[/tex]
Now that we know what x is equal to we can plug it into the blue equation to solve for what y is equal to
[tex]y = 2(4) - 6 \\ y = 8 - 6 \\ y = 2[/tex]
The place where the two lines intersect is at the coordinate (4,2)
