Extending classes can only be done with one class per class. It only means "this class will inherit all the methods from the class it extends". What you usually want when you extend a JFrame is to have the class itself be the contentpane for the things happening. What you want when you extend JPanel is usually to draw something within the panel itself. Just make another class called SuperPanel or something which in turn extends JPanel and then create a SuperPanel instead of the JPanel.
Easiest way to graphically output the array would probably be to create 4*4 JLabels, put them in a gridlayout inside a panel with the layout GridLayout(4,4) and then put the text ont he labels to element[0][1], [0,2] etc.
public class SuperPanel extends JPanel{
@Override
public class paint(graphics g){
//Things you want to draw here.
}
}
Something like that, dont have an IDE on this comp so youll want to check that out before using it, and ofc add things to the paint method. A good tip for this sort of thing would be to initially never extend anything, most things are doable without extending and its good practice to be able to code without extending, since itll make your life so much easier when you actually do start extending.
Hope this helps, gonna go be hung over again.