As you progress through Hogwarts Legacy, you’ll receive assignments from Professor Hecat, who can be found in the Defense Against the Dark Arts classroom in The Astronomy Wing. You’ll receive the first assignment during the Find the Secret in the Restricted Section main quest. Below are walkthroughs for these assignments.
Assignment I
Obtained: This assignment is automatically received as part of the story and is mandatory.
For the first task, you’ll need to win two rounds of Crossed Wands. You’ll also have to do a round of spell combination practice with Lucan Brattleby. Both side quests can be started at the Clock Tower Courtyard in The South Wing. If you already completed Crossed Wands: Round 1 then you’ll receive credit for winning one of the two. You can find a guide for the Crossed Wands side quests here along with a guide on Spell Combination Practice here. Once you complete both tasks, return to Professor Hecat and speak with her to begin the mini-game to perform the Incendio spell via wand movement. Learning the spell will complete the assignment.
Assignment 2
Obtained: The second assignment becomes available after bringing Professor Fig the book you got from the restricted section.
Professor Hecat will send you a letter via OWL with the next set of tasks for this assignment. You’ll need to successfully avoid enemy attacks by rolling 10 times and cast Incendio on 5 enemies. You can take care of most of the Incendio ones by doing the next Spell Combination Practice side quest. For what’s left you can exit the school ground and explore the surrounding area to find enemies to set ablaze or attacks to dodge. Once both tasks are complete, travel to Professor Hecat in the Defense Against the Dark Arts classroom during the day to attend class. When it ends, speak to the professor and she’ll teach you the Expelliarmus spell.