Texas>3days Macao>4 days Beijing>Texas eligible?

I'm flying from Texas to arrive in Macau on the 5th of September. I will fly from Macau to Beijing on the 8th of September spend several days there and fly out of Beijing back to Texas on the 12th of September.
*Does the clock start in Macau or Beijing?

Do I qualify for the 144 hour Visa free exemption so I don't miss my flight out of Beijing? Thank you for your help. This is a bit confusing & I'm afraid of making a mistake.