Were there any errors noted during the upgrade, particularly during installation of the HTML module or any of the Telerik components?
Please check the Admin --> Event Viewer for any related errors that are being logged and which may give more information.
When logged in as host user, navigate to Host --> Extensions, find the Html module in the list of Installed Modules. What version number is shown?
Please check the web.config file to determine which editor provider is set as the default provider - to do so, look for the following element:
<htmlEditor defaultProvider="DotNetNuke.RadEditorProvider">
In this example the default provider is the "DotNetNuke.RadEditorProvider". Your default may be different - possibly FckHtmlEditorProvider or TelerikEditorProvider.
Please check the site's /bin folder to determine the version of the assembly: DotNetNuke.Modules.Html.dll. If your install is on a local machine you should be able to hover the mouse over this file read off the file version. If it is a remote installation you will first need to download this file via FTP, etc. to examine it.
Finally, when upgrading from 4.4.0, what was the sequence of versions through which you upgraded to get to 6.0.0?