Android Question Permissions to write in Android 4, 6, 7, 9?

I'm working on an educational project that needs a directory in the root of the tablet, where users (teachers, parents, the pupil him- herself) can put an additional picture or textfile. For that reason the app starts with creating that directory. file.makedir(File.Dirrootexternal.....etc It works fine on an old smartphone (Android 4) and on newer ones too. (Android 7 and 9) But it does not work on an older tablet (Android 6).
In the Manifest Editor I added these lines:
android.permission.WRITE_EXTERNAL_STORAGE
android.permission.READ_EXTERNAL_STORAGE
What else can I do?