First of all, there are several ways of integrating FileMaker with MySQL.
The easiest way is to connect your FileMaker Database to your MySQL database via ESS.
For that you will need to setup ODBC drivers and I encourage you to use a FileMaker server, if you are not already doing that.
When you have connected, you can add the MySQL tables to your relationship graph and work with them as if they were a part of the FileMaker Database.
Please go to filemaker.com->Support->Downloads to find documentation about setting up ODBC and ESS.
Yes, It's easy via ESS. But As I mentioned, I have same tables on both database [ I think with ESS, MySQL tables would be appeared in Filemaker ].
Is it possible to exchange data between same tables instead of using common table for both.
Let me know if I should describe more.
If you are connected thru ESS, and see both the internal and external tables in FileMaker, you should be able to write a script to do the sync
This also may help, and supports MySQL:
I use FileMaker as a front end for our mySQL back-end database, and it works really well via ODBC. I don't have the mySQL tables duplicated in FM, and it is not necessary (or desireable) in my application.
Alternatives include using FileMaker Server, to "pull in" the mySQL data into FM on a batch basis, or to create an ODBC connection between FileMaker Server and mySQL for real-time two-way connections.
Real syncing, with transaction integrity etc. is pretty complex, and the 360Works plugin is proably the way to go if you need that kind of functionality.