The Permissions tab shows permissions specifically assigned to an author that are not inherited from group membership. This author has no specific permissions assigned.
Ekramer has Read permission for the System folder, but it does not appear because it is inherited from group membership in the HR Team.
Authors who are members of the HR Team group cannot modify publishing styles since they have Read permission for the System folder, which includes the Styles folder. However, you want to allow this author to modify publishing styles.