Find out where your class file is ending up. I don't know how NetBeans works. Does it place the class file in the same directory as the source? Does it put it in it's own directory, ie classes/NeHexx or bin/NeHexx. Are you using the package declaration or is it in the default package? Here is a scenario:
NeHe06.java is in package NeHe06 so it will be in directory - c:\Java\src\NeHe06. When you compile, the class file is in c:\Java\classes\NeHe06. In this case, the texture needs to be in c:\Java\classes\data. Then the absolute path works. Even if you are using the default package or a package that is 6 deep, the texture would still be in the same spot.