Hello malcolm229,
Welcome to the Apple Support Communities!
It sounds like you were previously running iOS 10 beta and are now having issues updating your iPhone to the public release of iOS 10. We can see that you iPhone appears to be in recovery mode as well and you are unable to move forward.
We know that unexpected situations like aren't optimal, but we're here to help!
At this point, if you have not done so already, you may need to follow the steps in the article below to restore your iPhone and get it running the public release of iOS 10.
About iOS beta software - Apple Support
If you're using iOS beta and want to go back to the current version of iOS, follow these steps:
- Make sure that you're using the latest version of iTunes.
- Put your device in recovery mode and restore it. If you turned on Find My iPhone, enter your Apple ID and password after the restore to activate your device.
- If you can't finish the restore, get help.
- After the restore is complete, you can set up your device from your archived backup. This backup should be from an earlier version of iOS.

If your device has a prerelease version of iOS and you restore the device to an earlier version of iOS, you might not be able to restore your backup. This can happen if the backup is from a later version of iOS. For example, if you restore your device to the current version of iOS and try to use a backup that you created using a prerelease version of iOS.
We realize that your iPhone is already showing the Connect to iTunes graphic on the display, but work through the steps as described here to try and resolve the issue.
Have a great day