I'm not sure converting to feet is going to work better for you. To get k, you just divide: F=kx, so k=F/x=8 lb/8 in = 1 lb/in.
Work is positive if the force is in the same direction as the change in length and negative if the force is in the opposite direction as the change in length.
So in (a), you should have the integral from 2 to 8 of kx dx. The x is the change in length from its rest position, so (18-16) to (24-16). The force is in the expanding direction and the change in length is in the expanding direction.
In (b), you should have the integral from 0 to -4 of kx dx. Now the force is in the contracting direction and the change in length is in the contracting direction.
In either case you are doing work on the spring, so the answer is positive.