Cheapest flight from Phoenix, Az, USA to Shenyang, China?

No direct flights are operating from Phoenix to Shenyang, China. However, you could take flight to San Francisco first, then to Beijing, China and last to Shenyang by flight or bullet train. About the flight from Phoenix to San Francisco and San Francisco to Beijing, you would better consult the booking agencies there, as the international airfare is always cheaper at the departure city.