I have been downloading fonts from this website for YEARS! I have never had a problem....until today. I downloaded a font I can see it my downloaded files, but I cannot open the files and therefore cannot install the font.....PLEASE HELP

In your pic, the font is compressed in a zip file.
Did you try to drag it from the ZIP file to your desktop?

Yes. I have moved it to my desktop. I’ve tried double clicking on it. I have right clicked on it and selected open. Nothing opens the file.

Double click on the font. TTF or OTF? It is your choice. The double click opens the font in Windows' default font viewer. You will see two buttons near the upper left corner of the preview window - one is Print and the other is Install. Click on Install and wait for the installation to complete. Then close the Window. Open the application where you want to use the font. If it was already opened before you installed the font, close that program and then open it again. See if the font is now listed in font menu. It should be there.

You can now use the font in any program that you have in your computer that is able to use any fonts installed in your PC.