I think it should say, "10lbs of"If a spring needs 10lbs of work in order to keep it stretched 4 inches from it's natural length, how much work is need it to stretch it to 6 inches from it's natural length?"force."

In Hooke's law, you don't count the natural length, so 4 inches is the displacement of the spring's end from its equilibrium position. Thus, 10 = 4k, from where k can be found.

The work needed to stretch the spring to 6 inches from it's natural length is (up to the sign) .