Assignment 1
You’ll receive the first assignment for Professor Garlick from an owl post after learning the Confingo spell during the main story. She will task you with obtaining a Venomous Tenatcula and using it. She will also ask you to get a Mandrake and use it on multiple enemies at the same time. Both of these items can be purchased from Dogweed and Deathcap in the north part of Hogsmeade. The Venomous Tenatcula costs 600 gold and the Mandrake costs 500. After collecting the items, head out to the world map and use the items to satisfy the task condition. You’ll then need to attend Herbology Class in the Library Annex during the day. After the class, speak with Professor Garlick to learn Wingardium Leviosa.
Assignment 2
The second assignment will unlock shortly after completing the first one as time passes. Professor Garlick will give you the task of growing and harvesting Fluxweed. You’ll also need to acquire a Mandrake, Chinese Chomping Cabbage and Venomous Tentacula then use them all three simultaneously. You can buy the seeds for the Fluxweed from The Magic Neep. You’ll also need to buy a Table with a Large Pot from Tomes and Scrolls. Both shops can be found in Hogsmeade. Next head to the Room of Requirement and conjure the table then interact with it and plant the Fluxweed seeds. It will take 15 minutes for the seeds to grow. Then you can harvest the plant to satisfy the first task. For the second buy all three items from Dogweed and Deathcap. You can then use all three items simultaneously (without any enemies) to satisfy the second task. With both tasks complete, return to the professor and speak with her in one of the greenhouses to learn Flipendo.