Answer
the objective function has minimum value 8 at (0,4)
the objective function has maximum value 16 at (0,8)
Work Step by Step
The region that is defined by the constraints is
* to the right of x=0 (the y=axis),
* above the line y=0 (the x-axis),
* below the line 2x+y=8,
(for this line, when x=0, y=8 and when y=0, x=4)
* above the line x+y=4
(for this line, when x=0, y=4 and when y=0, x=4)
The region is shaded red on the image below.
The corners are (0,8), (4,0), (0,4).
Calculating the objective function z=3x+2y in each corner point,
(table in step 6 of the image)
we find that
the objective function has minimum value 8 at (0,4)
the objective function has maximum value 16 at (0,8)