If you have manager-level security access, you are able to create projects for other managers, but when you save them, you get an error that you don't have the permission to view this record. This happens because, by default, managers can only see the projects managed by them in the Projects list view. So, although you can create projects for other managers, you won't be able to view them afterward because of the security restrictions.
If you want to view the projects of other managers, you need to get your security permissions customized by checking the option Allow access to other managers data under Project in the Security > Customize Profile screen. Contact your Core administrator for that. Check the Core Help for details on customizing security permissions.