Hi,
I am not quite sure what you want to achieve, it would be best if you could provide me some additinonal information or maybe some screenshots.
However if you go to the page, where you want to move web part zone, you need to edit layout of the page (icon in a green stripe). There are listed web part zone used on the page and you can simply move them by moving them in the layout code.
I would recommend you to read our Portal Engine tutorial
http://devnet.kentico.com/docs/tutorial/index.html. I believe you will find there a lot of useful information.
Best Regards,
Roman Konicek