There are a whole bunch of programs which use the extension "PDE": Arduino use one, PowerDesk also, and there are others.
So "run .pde" file is not a single process, but instead is controlled by teh software installed on the PC.
However, this may work:
Process.Start(@"D:\Temp\MyFile.pde");
If an application is installed which "knows about" files with the extension "PDE" then it should run and open the file. If not, then you're pretty much on your own - you will need to examine the file, and where you got it from in order to work out just what to do with it.