Look for the file called com.apple.springboard.plist and open it in Property List Editor.
The file should have a key titled SBParentalControlsPin and the Value for this item is exactly what we were looking for. Our missing 4 digit Restrictions Passcode.
To carry off this hack, you need to be using unencrypted backups of the device (otherwise, you won’t be able to read the file). Or, naturally, it’s very easy if you have a jailbroken device.