How can I delete this folder?

So, back when I last reformatted my computer I decided it was a good idea to have a backup just in case. It was good cause after the restore I was able to recover some of my pictures and whatnot. But now, I have exhausted all I want from the folder, but I can't delete it. The remainder of the contents take up around 4gb of memory, and I really want that memory because I only have a 80gb HD. If you have any ideas on how I can get rid of it, aside from a reformat, that'd be great.

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