How do I use a power adapter extension cable?
The picture in your question is referred to as an AC wall adapter, or "duckhead" (US) and slides out of the AC power adapter so you can then slide in the AC power cable (US), pictured in the link in your question.

The picture below shows the "duck head" being slid out of the AC power adapter and once removed the AC power cable gets slid in its place, thus providing an extension cord to the AC power adapter.