List subfolders of a specific asset folder
Not a complete answer, but in your example image if going to be an instance of AssetFileModel.

AssetFileModel has a getFolder method that returns an instance of AssetFolderModel.

AssetFolderModel has a getChildren method you could loop through to get all of the subfolders for the given folder.

Depending on how numerous your file/folder structure is, though, it might be more efficient to do this from PHP in a custom plugin rather than to do it from Twig.