Answer
See below.
Work Step by Step
We evaluate $z$ at the corner points:
$(0,6):z=2(0)+3(6)=18$
$(5,6):z=2(5)+3(6)=28$
$(5,2):z=2(5)+3(2)=16$
$(4,0):z=2(4)+3(0)=8$
$(0,3):z=2(0)+3(3)=9$
Thus the maximum value is $28$, the minimum value is $8$.