Anti-Gun Trafficking Penalties Enhancement Act of 2006 - Amends the Science, State, Justice, Commerce, and Related Agencies Appropriations Act, 2006 to repeal restrictions on disclosure of the content of the Firearms Trace System database. Directs the Attorney General to provide state and local governments or law enforcement agencies with information from such database upon receipt of a written request.

Requires federal law enforcement agencies investigating a crime to provide information about firearms stolen or used in such crime to the Bureau of Alcohol, Firearms, Tobacco, and Explosives (BAFTE).

Amends the Omnibus Crime Control and Safe Streets Act of 1968 to require state and local law enforcement agencies investigating a crime to provide information about firearms stolen or used in such crime to BAFTE.

Amends the federal criminal code to: (1) permit the Attorney General to inspect the inventory and records of a licensed importer, manufacturer, or dealer to insure compliance with recordkeeping requirements at any time (currently, not more than once in 12 months); (2) increase penalties for firearms violations; and (3) include illegal firearms sales and trafficking in the definition of racketeering activity.