At the common point of the lines x+y=4 and 2x=y-2, the x and y coordinates are equal.

2x = y - 2

=> y = 2x + 2

substitute in x + y = 4

=> x + 2x + 2 = 4

=> 3x = 2

=> x = 2/3

y = 4 - 2/3 = 10/3

**The common point of the lines is (2/3, 10/3)**

To determine the common point of the lines, we'll have to solve the system of the equations of the given lines.

We'll solve the system using substitution method. We'll change the 2nd equation into:

x+y = 4

x = 4 - y (3)

We'll substitute (3) in (1):

2(4 - y) = y -2

We'll remove the brackets and we'll subtract y both sides:

8 - 2y - y = -2

We'll combine like terms and we'll subtract 8 both sides:

-3y = -2 - 8

-3y = -10

We'll divide by -3:

**y = 10/3**

We'll substitute y in (3):

x = 4 - 10/3

x = (12-10)/3

**x = 2/3**

**For the common point: The solutions of the system represents the coordinates of the intercepting point of the lines: {(2/3 ; 10/3)}.**