All users except collaborators can delete folders by sending them to the Recycle bin. Only admins can permanently delete folders.
When you delete a folder that has tasks, subtasks, subfolders, and subprojects:
If those items are only located in that folder then they're deleted when the parent folder or project is deleted.
If those items are stored in additional locations, then they'll continue to live in those additional locations even after the folder is deleted.
Deleting a folder moves it to your Recycle bin, where it can be permanently erased or restored. This can be done in two ways.
Navigate to the space containing the relevant folder.
Right-click a folder from the left-hand navigation panel 1.
Select Delete from the drop-down list that appears 2.
Click Yes in the confirmation that appears 3.
Alternatively, you can:
Yes, admin users can permanently delete folders. After navigating to the Recycle bin, they can right-click a folder title in the left-hand navigation panel and click Erase. Or, they can open the folder info panel from the Recycle bin and click Erase in the top right corner of the panel.