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While you may have installed in the root of your public folder you probably did not actually install to the root of your hosting area. Most decent hosting has areas you can access outside of your public folder. All public folder means is what can be accessed via a browser on the internet.
From the path, Folder /home/thdradmi/public_html/xoops_data, we can see that the above is your case. You would want to move the Xoops data to the 'thdradmi' folder. This is good security as these files are then in an area that can not be reached by an outside browser. You will need an FTP client to do this. I suggest Filezilla.
Someone else is going to have to tell you what configuration files you are going to have to edit to reflect the move.
To be honest, unless you have done a lot already, I think it would be easier to just do a new install.
