is this on an outlook.com account? by outlook.com I mean that site hotmail, live and any of the many names the service has had in the past 20 years.

no this is, it is "allianceglobalservices.com" account

Are you able to select them to subscribe? right click on mail account name in folder pane and select 'Subscribe' select folder(s) and clickon OK

what happens? Describe what you see when you clickto see the 'Subscribe ' window.

Is the mail hosted on office365. If so get your administrator to follow the incident I reference in my blog post.

@Toad-Hall : when I open subscribe folder, I am able to see my sub folders. after check the my sub folders and click on subscribe and close the window.

I am expected to see my sub folders, but still those are not displaying

@Matt: Yes Matt, it is hosted with office365

It would appear that Microsoft released a bad update to their office365 / outlook.com servers which broke IMAP folders. Microsoft are working on the issue and promise to remediate the situation. For a workaround, please see my blog post. Unfortunately other an that there is nothing more we can offer until Microsoft fix their servers,

We are tracking this issue in Bug 1241926.