I am confused whether I can use this above extension used in the ArcGIS Desktop Standard or ArcGIS Desktop Advanced
Yes, the 3D analyst provides functionality to any level of ArcMap, the extension does not require a particular licence since it adds its own capabilities to work with 3d data
Adding to Dan, the license of 3D Analyst extension needs to be purchased additionally(if not yet purchased). Then you could use the extension along with any ArcGIS Desktop license level.
Once the license is available, you need to enable the extension from Customize > Extensions in ArcMap.