The net current passing through loop e flows in a clockwise direction.
Since loop e passes through the boundary between regions II and III, the magnetic field it encloses is spatially varying. This means that the line integral of the magnetic field around loop e is not zero.
According to Ampere's law, this means that a net current must pass through loop e.
The direction of the net current can be determined using Lenz's law. Lenz's law states that the direction of the induced current in a loop is such that it opposes the change in magnetic flux through the loop.
In this case, the magnetic field is increasing in magnitude from region II to region III. Therefore, the induced current in loop e must flow in a direction that creates a magnetic field that opposes this increase.
The right-hand rule can be used to determine the direction of the magnetic field created by a current-carrying loop. If you curl your right hand around the loop with your fingers pointing in the direction of the current, your thumb will point in the direction of the magnetic field.
In this case, the current in loop e must flow in a clockwise direction to create a magnetic field that opposes the increase in magnetic flux.