To help, have a look at some images I posted to
this thread some time back.
They were taken with my FZ10 - which has the same lens as the FZ20 - and they show the same thing at zero zoom, the full 12X and then, just for the heck of it, the 12X optical with 3X digital thrown in.
That's the sort of difference the lens can make.
As for adding a converter lens to a 3X zoom, I'm not sure that any camera like that can handle one. Some might but it's difficult to imagine how they might be fitted. But I've no doubt that you're asking the question on the right site. If it can be done, there's someone here who will be able to tell you how to do it.