I assume that the program, that you are referring to is Adobe Premiere Elements 8, since Photoshop Elements does not have Projects, per se.
If so, then much will depend on how you set up your Premiere Elements 8 Project. If you created a folder for your Project, and then created sub-folders, below your Project's folder, it is a simple matter of just Deleting the Project folder, and everything else will be Deleted, as well.
If you did not setup your Project that way, you will need to do a bit of Searching, via Project Names, and then by file names.
Also, if you think that you would ever need to revisit that Project, you might want to explore using the Project Archiver first, before you Delete.