Am I eligible for 144 hour free visa ?

Yes, you can do that by using 144 hour visa free transit.

You should take care that your itinerary is:

Vietnam - Beijing - Hong Kong - Vietnam

Also, you should be aware that you are not allowed to have any additional landing between Vietnam and Beijing and Beijing and Hong Kong in order to be eligible for 144 hour visa free transit scheme in wider Beijing area. In other words, the flights on the mentioned routes have to be nonstop flights.

You are allowed to stay in Beijing for 144 hours counting from the day following the day of your arrival. In other words, if you arrive on Thursday, you are allowed to stay in Beijing until the end of Wednesday. You can stay in Hong Kong more than that because Hong Kong has separate and different immigration policy compared to mainland China.