When you accidentally archive a photo instead of deleting it on Instagram...

1. Go you your profile by clicking the icon at the lower right of the main navigation that looks a head and shoulders.
2. Click the icon at the upper right that looks like an arrow going in a circle counterclockwise with clock hands inside of it.
3. At the top of page that appears that says "Archive" click on the "Archive" title to get options.
4. Amongst the options are "Posts" and you should pick that.
5. Delete the thing you archived.