which picture shows an example of no work being done?

Brief Explanations:

Work is done when a force causes an object to move in the direction of the force. In the case of a person holding a heavy object without moving it vertically (the third picture where the boy is trying to lift a barbell but it isn't moving up), no work is done as there is no displacement in the direction of the force applied. In the other pictures, there are displacements due to applied forces (lifting a child, pushing a cart, pulling a suitcase while walking).

Answer:

The third picture (the boy trying to lift the barbell but not moving it vertically)