One of the user is not able to see the Availability of any of the Video Conferencing Room Mailbox under Calender option, When He is trying to Book A room he is getting Completely Greyed out in front of the Room Mailbox. 

Have the user try to start Outlook with the /cleanfreebusy switch, and see if he can see free/busy of the Video Conf Room.

outlook.exe /cleanfreebusy

Can the user see availability of other individuals?  If so, you might need to check the availability of the VC room.  Open the VC Mailbox, right click on Calendar -> Properties -> Permissions Tab, and see what "Default" permission level is.

Hi,

According to your description, I understood the issue occurred on one specific user.

Does the user book A room normally on OWA?

Please refer to DJStatik's response to check the permission.

If the permission is normal, we can try to run outlook under online mode to test.

Regards,

David