Assume that the pictured magnet is being moved into the solenoid. If the polarity of the magnet is reversed and then moved into the solenoid, what happens? *

The direction of induced emf is revered and hence the direction of the induced current.

Explanation:

If the polarity of the magnet is reversed, the direction if the field lines through the solenoid is also reversed, which according to Faraday's law means

in other words, the direction of the magnetic flux is revered, and therefore, the direction of the induced emf is also revered.

Furthermore, according to Ohm's law

which tells us that if the induced emf changes sign (is reversed)

the direction of the induced current is also reversed.