We want to minimize p=x-2y, given the constraints. This means we want x to be as small as possible and y to be as large as possible, since this will minimize p.
The fact that x ≤ 8 and y ≥ 0 means we are free to set x as low and y as high as possible, as long as they agree with the other constraints.
Graphing the inequalities helps to see the optimum point. It is where 3x +2 and -x +10 intersect, at (2,8). This is the greatest point for y that agrees with our inequality.
Remember that the function we are minimizing is p = x - 2y
The value for p at this point is 2 - 2(8) = 2 - 16 = -14
Answer is D)