How do you complete buck's quest in pearl?

To complete Buck's quest in Pokemon Pearl, you need to first defeat Team Galactic in the Galactic Eterna Building. After that, Buck will give you the Storage Key to use in the Galactic Warehouse. Use the key to access the warehouse, battle your way through, and defeat Team Galactic Commander Jupiter. Once you defeat Jupiter, Buck will thank you for your help and the quest will be completed.