Answer :
The general formula to calculate the work is:
[tex] W=Fd \cos \theta [/tex]
where F is the force, d is the displacement of the couch, and [tex] \theta [/tex] is the angle between the direction of the force and the displacement. Let's apply this formula to the different parts of the problem.
(a) Work done by you: in this case, the force applied is parallel to the displacement of the couch, so [tex] \theta=0^{\circ} [/tex] and [tex] \cos \theta=1 [/tex], therefore the work is just equal to the product between the horizontal force you apply to push the couch and the distance the couch has been moved:
[tex] W=Fd=(220.0 N)(3.9 m)=858 J [/tex]
(b) work done by the frictional force: the frictional force has opposite direction to the displacement, therefore [tex] \theta=180^{\circ} [/tex] and [tex] \cos \theta=-1 [/tex]. Therefore, we must include a negative sign when we calculate the work done by the frictional force:
[tex] W=-Fd=-(144.0 N)(3.9 m)=-561.6 J [/tex]
(c) The work done by gravity is zero. In fact, gravity (which points downwards) is perpendicular to the displacement of the couch (which is horizontal), therefore [tex] \theta=90^{\circ} [/tex] and [tex] \cos \theta=0 [/tex]: this means
[tex] W=0 [/tex].
(d) Work done by the net force:
The net force is the difference between the horizontal force applied by you and the frictional force:
[tex] F=220 N-144 N=76 N [/tex]
And the net force is in the same direction of the displacement, so [tex] \theta=0^{\circ} [/tex] and [tex] \cos \theta=1 [/tex] and the work done is
[tex] W=Fd=(76 N)(3.9 m)=296.4 J [/tex]