There are several versions of L4D2 available for download right now but updating it to be able to work on Garena is the same.

Install the following in the correct order.
Patching to v2.0.0.7
Install this v2.0.0.7 file to your root L4D2 directory. Eg. C:\Program Files\Left4Dead2\

Patching standalone
Install the L4D2SP 1.G file to your root L4D2 directory also.
Installing the standalone will prompt you to choose your nickname for the game. Alternatively you can change it by looking at some ini files eg: stryder.ini for me, or use console, setinfo name NEWNICK

Setup Garena
Enter L4D2 room and go under settings. Select the left4dead.exe, and choose it as your Executable Setting.

Next, for Game Boostrap Parameters. Enter: +sv_allow_lobby_connect_only 0 +sv_lan 1
It should look something like this.

Have Fun !