Download from the FileZilla site both the client and the server versions.
Install on your computer the server version set a default serving file directory and to put the files that you want to transfer in the Directory.
If your brother has any FTP client program he can use it, otherwise tell him to download and install the FileZilla FTP client program.
On your computer, you have to open Ports 20-21 through the Firewall, and or Router.
Log to
http://www.whatismyip.com to find your external IP. Email the external IP number to your brother. Make sure that your FTP server is running.
Your brother should start is FTP program and enter your external IP as the server address. If every thing set correctly, his ftp program would connect to your ftp server and he would be able to download the files.
The above is the general principle you should read the programs instructions to set every thing correctly.
If you would like to set a system with more a capacity to always when needed to be connect to this page might help,
Connecting to a Computer/Server/Network through the Internet
If you prefer using the Ultr@VNC method that was mentioned in few posts above this might help as well,
Ultr@VNC (Remote Control for your Network/Internet) - Installation, and Settings
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P.S. You need to set such an arrangement only one time and it can server well in the future.
If your brother needs to transfer file to you, the same arrangement cab be used he can use the FTP client to upload the files to your FTP server.