Question: I would like to do something like play.clubpenguin.com. 

What it does is that, when you visit the site, maybe using firefox or IE, if you opened a new tab or use other browser, when you visit that site again, it will show something like: "Please close the other browser that opened this page" or something like that. 

How to do this? (Its client's request)

More information: The site is Flash site

EDIT: 

Ok, i think this is a tough question, well, in general, Can this be done using php, mysql and JS?

Answer: 
Each time you serve the flash page to the user, generate a random token. Embed this token somewhere in the page, for example as a flashVar. Also, store the most recently generated token in the user's session.

Whenever the flash posts something back to the server, post the token as well. If the token does not match the token stored in the session, reject the post.

That way, only the most recently generated version of the page will have the ability to communicate with the server and if the user opens multiple versions of the page only the most recent will work.

This technique should work even if the user opens extra browsers on other machines. It doesn't use IP addresses to establish identity. And there is no chance that a user will somehow be 'locked out' permanently because every time they open the page again you reset the stored token.

It's a similar idea to the way some frameworks insert a validation token into forms to prevent [Cross-site Request Forgery](http://en.wikipedia.org/wiki/Cross-site_request_forgery) attacks.
If you want to forbid access with 2 different logins, you can enforce a rule that lock on a given resource. 

The client IP could be one of this lockable ressource: only one session allowed for one given IP address. That would reduce the cheating to people that have multiple public IP addresses. People that shares public IP through proxy would have problem.

I don't see what other lockable resource you can use easily.