Percival Rackham's Trial is a key quest in Hogwarts Legacy, which is somewhat tricky in several ways. One of the most difficult objectives is to "complete Percival Rackham's trial," which involves you exploring a magical maze beneath the tower where you found Rackham's painting, and there are many moving platforms and magical pathways to contend with.
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How to Finish Percival Rackham's Trial
Completeing this task does not entail completing the Percival Rackham's Trial quest (you must defeat a boss to complete this), but solving all of the moving platform puzzles will satisfy this objective.
The first platform puzzle is fairly straightforward. Using Accio, you will need to move the platform to the left, then investigate the ancient magic to open the archway. Return the platform, pull it past the archway, and jump off behind the archway.
Go down the steps below the platform, then up the stairs to the right. The ancient magic is hanging in thin air, so you need to remove the platform so that you may explore the ancient magic.
Next, go through the archway from south to north so that the bridge disappears. Then go to the south side of the chamber and pull the platform all the way over to you. Return to the bridge, climb on it, and take the platform up to the exit on the south side.
After defeating some Pensieve Protectors, the third, final, and most challenging platform puzzle begins. Look for the ancient magic, then draw the platform toward you and jump onto it. Use the hook behind the archway to draw yourself a little closer to the archway but not beyond it.
Next, get your left hand side of the chamber, but not all the way over to the left. You want to stop as close to the archway as possible. Use Accio on the platform that you can see through the archway, and both platforms will be pulled straight up to the archway so that you may jump through it onto the other platform.