The work done by a force equal to F when it acts over a distance d is equal to W = F*d.
The frictional force encountered in sliding the chest is equal to 64 N. This has to be overcome to move the chest. As the chest has to be moved across a distance of 4 m, the work that is required to be done against the force of friction is equal to 64*4 = 256 J
The work done against the force of friction equal to 64 N to slide a chest by 4 m is equal to 256 J.
We know that the the force we apply to the chest is opposite to the direction of the frictional force.
The force applied to the chest would have to be greater than the frictional force in order to make it slide across the floor. So the force applied must be greater than 64N.
Work = Force x distance
Force > 64N
distance = 4m
Work > 64N x 4m > 256 Nm
Therefore, the work done in sliding a chest 4m across the floor would be greater than 256Nm.