144 hour visa pass

Can I go from LAX, August 13, arrive in Beijing August 14 (with a short stop over in Hong Kong), stay in Beijing until August 20 (6 days), then leave Beijing on August 20 to Hong Kong on August 20, and theb leave Hong Kong on August 27 to LAX? Would the 144 hour free transit apply? If yes, should I notify my airline before I board in LAX on August 13? Or do I just go to the 144 hour free transit desk when I arrive in Beijing?