Every Hangout has a special photo album that you can access through Picasa Web Albums ( http://picasaweb.google.com
) or Google+ Photos (if you use Google+).
You will not be able to delete a photo shared by someone else in a Hangout chat – they would have to delete that image themselves.
If you downloaded the Hangouts image to your computer or phone, you should be able to find and delete it in the Downloads folder.
You can also read more here: http://www.peggyktc.com/2015/06/find-your-hangouts-photos.html