Lightroom is NOT a file browser. You only see files that have been IMPORTED into Lightroom and the file you exported is not automatically imported unless you tell Lightroom to import in the export dialog by checking 'Add to This Catalog'
Instead of reimporting you can change the Post Processing to "Show in Finder" or what ever the Windows version is and see the photo using the OS. I usually consider the exported files as a temporary file for a specific use so don't import them.
I've already properly imported the files - we use it as our archives so I import it once and export them post-edit to 4 different folders. At this point, I can edit the photo after importing, and export in theory. However, after doing everything in the screen shot you sent, the files aren't visible in the folder I set as my "export to" location in LR. They are, however, visible if I open the file from my desktop. Thoughts?
You need to reread my post about Lightroom NOT being a disk file browser. If you want to see the photos you have exported to the 4 different folders in Lightroom than you will have to import the 4 exported files into Lightroom (which I think is a bad idea) or check the "add to catalog" button and Lightroom will do it for you. For my interest, why are you exporting to 4 different folders? For me, if I need a derivative file from the one in the catalog I can just export it again and if these are 4 different renditions of the same photo than I just use virtual copies in Lightroom.