It's the folder that you specified during the installation. Most people don't change it, so the client should have been installed to the default location, C:\Program Files\Gravity\RO, or C:\Program Files (x86)\Gravity\RO if you're using a 64-bit Windows, or anything similar.
If you REALLY do not know where the folder is, then
right click on the "anthem game client" you speak of (I assume the one in the start menu or on your desktop?), choose "Properties," then "Shortcut," and check the path next to "Target," like in this screenshot:
http://tux.human.cornell.edu/help/Images/properties_shortcut.gif
