Do I qualify for a 72-hour Visa free transit

I am travelling from USA to Thailand. I plan to fly to Guangzhou on the way back to visit my daughter who is working there. I would stay in the Guangdong province and arrive Monday late afternoon and depart the same Thursday morning (so under the 72 hour limit). However, my flight back to USA has a stop and 4 hour layover in Beijing. I cannot tell by reading the procedures if this would be acceptable.

THANKS!