May I confirm if I do a trip from Macau -> Beijing -> HK, will I enjoy the 72 hour visa free please?

Hi, Tammy.
Personally speaking, you can easily get rejected when you apply for a 72-hour free transit, because your trip may be easily regarded as a round trip for the Macau and HK at the same area.

But it is still suggested to consult with Beijing immigration at the airport and their phone number is 0086-10-56095400.