Hi Charles,
libwebkitgtk-3.0 is not supported by Eclipse.
I can't see the attached screenshot for some reason, but if it says that WebKit is not installed, you should install libwebkitgtk-1.0-0:
> sudo apt-get install libwebkitgtk-1.0-0
If it does not help, could you please run Eclipse from the terminal and post console output to this thread?