Both folders and quizzes can be deleted and doing so will place them in the Trash. Any deleted folders can be restored within 30 days. After the 30 days, they'll be permanently deleted and cannot be restored.
Delete a Folder
Go to your Quizzes tab:
Select the folder you'd like to delete and click Delete. The folder will then be moved to Trash.
Restore a Folder
While in the Quizzes tab, go to Trash:
Select the folder you'd like to restore and click Restore. The folder will then be available in your quiz list again. Keep in mind, you can only restore folders within 30 days. After 30 days, they'll be permanently deleted and cannot be restored.