Regarding 144 hour-visa-free policy

Hello, I have a question about a visa-free policy.

I am a South Korean passport holder. I would like to ask you if the below itinerary can be eligible for a 144-hour-visa-free policy.

Taipei > Hong Kong > Wuhan > Macao > Taipei

1) Can this itinerary be eligible for a 144-hour-visa-free policy?
2) In this case, do I need to exit the Hong Kong airport & the Macao airport? Or can I just stay at the airport and transfer to the next airplane? (So, in this itinerary, which city counts as my departure and arrival? Is it Hong Kong and Macao?)

Thank you so much!