When you take a backup on your computer's iTunes it will overwrite the previous backup, so you will usually only have the one backup - I've had multiple backups listed when I've updated the iOS version, in which case I've had a pre-update and a post-update backup listed. Any backups that you have should be listed in the Devices tab in Edit > Preferences (iTunes > Preferences if using a Mac) on your computer, or you can view them via windows explorer (finder on a Mac) :
- Mac: ~/Library/Application Support/MobileSync/Backup/
The "~" represents your Home folder. If you don't see Library in your Home folder, hold Option and click the Go menu.
- Windows XP:\Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\
To quickly access the Application Data folder, click Start, and choose Run. Type %appdata% and click OK.
- Windows Vista, Windows 7, and Windows 8:\Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\
To quickly access the AppData folder, click Start. In the search bar, type %appdata% and press Return.
If it's not listed there then it is no longer on your computer. If you hadn't also been backing up to the cloud then you could try searching for programs that claim to be able to recover content from a device (and see if any can recover documents from apps, not just photos), but you have probably lost any documents that you had on it.
