The given system of inequalities is equivalent to 


y >= 8 - 2x          (1)

y >=            (2)

y <= 6 - x           (3)


The plot below represents line (1) in red, line (2) in green and line (3) in blue.






Plot y = 8 - 2x (red), y =  (green) and y = 6 - x (blue).



The solution to inequality (1) is the set of all points belonging to the half plane above the red line (including points of this line).

The solution to inequality (2) is the set of all points belonging to the half plane above the green line (including points of this line).

The solution to inequality (3) is the set of all points belonging to the half plane below the blue line (including points of this line).


The solution to the given system of inequalities (1), 2) and (3) is the intersection of the sets described above.


Thus the solution to the given system is the set of points belonging to the triangle which is ABOVE the red line, 
ABOVE the green line and BELOW the blue line.


Again: the solution is the set of points of the triangle which is restrained/confined by these three lines.