Connecting an iPod Touch 4th generation to a projector?
From the "Video Mirroring" section:


  You can use the Apple Digital AV Adapter or VGA Adapter to display the contents of your iPad 2 screen to a compatible TV, projector, or other external display.


Note that it explicitly says iPad 2. That is the only device which currently supports mirroring. While the 4th generation iPod touch supports the AV adapter, only applications with a video out mode will display anything through it. Most applications don't support video out, and won't display anything on the connected screen. If an application does support video out, it will usually mention it in the features list in the app store, so you can tell before you buy an app whether it will support it or not.