Q: I can't delete picture synced

You cannot delete one synced picture from your iOS device unless it was the only picture that you synced. If it is in a folder that you synced from your computer, you have to unsync the entire folder and then remove the photo that you do not want on the device from that folder and then sync that folder again.

See the section regarding deleting synced photos.

Sync photos from your computer to your iOS device using iTunes - Apple Support