Vietnam to China to Japan, is it really do-able with 144 hrs visa free?

Hi,
I'm still struggling to make sense of this 144 hour twov thing - Sorry! I hope somebody can give me some advice. I am a British citizen, planning a trip to Asia in the next month.
My plan is to fly from Vietnam (Hanoi) to China (Shanghai), stay in Shanghai for a couple of days, then fly to Japan (Tokyo). Then from Japan to Nepal a bit later.
If I stay for only five days in Shanghai, can I get this Free travel thing?
My main reason is because the Visa application process from the UK is driving me crazy and seems so expensive, £85 + 65 levies... Sigh.
Thank you for reading and for any help in advance.
Kindness,
Amy