I am able to connect from my computer (xp home edition)to my computer
(xp proffesional)with remote desktop. However I am not able to connect
from my Xp proffesional computer to my xp home edition with remote
deskop.
I have the same user name and password on both computers.
Under "remote" tap in system properties in xp home edition, there is
only the remote assistance information and nothing about remote
desktop.
I think the reason is that xp home edition only accepts remote
assistance. It does not accept remote desktop. Please let me know if
this is the case. Also is there any way to allow xp home editon to
accept remote desktop connection?

You are right that Windows XP home doesn't have the server component
of remote desktop connection (it comes with the client only).  You may
also want to look at
http://answers.google.com/answers/threadview?id=400001 as your
situation is somewhat similar (except that thread deals with Windows
2000 Pro - which also the same issue as WinXP Home).

To see how remote assistance works, please see
http://www.microsoft.com/windowsxp/using/helpandsupport/learnmore/remoteassist/intro.mspx

--
I am not an official GA researcher.