Object data panel menu, not available The panel that appears as shown in the image below, cannot be re-opened.
It only appears, on the left-hand-side of the screen when I create a new object.
How do I get it back as shown in the image?


https://wiki.blender.org/index.php/Dev:2.5/Source/Development/Proposals/Editable_Object_Parameters

My "Data" tab, looks different.
Judging from the (quite old) link you posted, that is just a proposal. No such feature has been implemented as far as I know.

As of version 2.77, once the original object has been created and has gone through some kind of transformation, there is no way to get the original creation parameters back.

Maybe it will get implemented in the future, maybe it will never happen...