In 10b) iv) when you sub y=12 you end up getting x = 6, and when you sub y=13 then you end up getting 2 2/3 and 27/2, so yeah, x lies between 6 and 2 2/3.
v) when you did da/dx and found the values when A'=0, it lies outside of 2 2/3 and 6, so the min area of KLM is at one of the end points...