To find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2, we first need to find the point of intersection of the two lines.

We can do this by solving the system of equations 2x - y = 4 and x + y = 2.

Adding the two equations, we get 3x = 6, so x = 2. Substituting this value of x into the equation x + y = 2, we get 2 + y = 2, so y = 0.

Therefore, the point of intersection of the two lines is (2,0).

Now we can use the distance formula to find the distance between the point Q (4,3) and the point (2,0).

The distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1,y1) and (x2,y2) are the coordinates of the two points. Substituting the values for x1, y1, x2, and y2, we get:

d = √((2 - 4)^2 + (0 - 3)^2) = √((-2)^2 + (-3)^2) = √(4 + 9) = √13.

So, the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2 is √13.