Can I fly from Hongkong to Beijing and then stay in Beijing for 78 hours

Debbie, yes, the 72 hours start from 00:00 the day following day of your entry date, so your actual stay in Beijing is more than 72 hours. But because you will travel back to HK after staying in Beijing, you cannot use the 72 hour free transit. According to the 72 hour policy, you should fly to a third country or region after transiting in a Chinese city.