P = 3x + 2y
There is an accompanying graph in this problem. In the graph, there are 4 points to consider. I'll just assign letters on each point.
Point O is found in x = 0 ; y = 0 or (0,0)
Point A is found in x = 8 ; y = 0 or (8,0)
Point B is found in x = 6 ; y = 5 or (6,5)
Point C is found in x = 0 ; y = 8 or (0,8)
We will substitute x and y in the equation by its values per point.
Point A = 3(8) + 2(0) = 24 + 0 = 24
Point B = 3(6) + 2(5) = 18 + 10 = 28
Point C = 3(0) + 2(8) = 0 + 16 = 16
The maximum value of the function P = 3x+2y is 28 and its minimum value is 16.