When you declare an anonymous class, you declare that it derives from a class or an interface. Therefore, you can call the methods of that class or interface on an object of the anonymous class, as you would for any other object.
If your anonymous class has any methods that are not part of the class or interface from which it descends, then you will only be able to call them from within the anonymous class.
Note that anonymous classes should not be great big classes anyway. If your anonymous class won't fit on a single editor screen, it's too big, and should be promoted to a proper named class.
Betty Rubble? Well, I would go with Betty... but I'd be thinking of Wilma.
I typically use a local class instead when I need to do this.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus