I have a few discussions in mysite.I want it to be moved to an other site.
Let me know how to accomplish this.
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You can save the discussion lists as templates with content, download them to your local machine, upload the templates to the desired site, and then create new lists from them.
I think Eric's answer is pretty much the best bet if you only have access to the Web UI, but unfortunately you do lose some information this way (things like correct "Created by" and "Created on" values as well as permissions).
There are numerous commercial content migration tools that can also handle this (things like Metalogix), but if you have access to one of the SharePoint servers and appropriate permissions you can also try something free like the Content Deployment Wizard