I am flying from Hunan To Guangzhou via Beijing. Does the 72 hrs begin from when we land in Beijing?

In your case, you'd better apply for a L type in advance. 72 hours free transit isn't ok.

The question is, I am flying from Toronto to Beijing and then onwards to Guangzhou, on Hunan Airlines, when does the 72 hours begin?

Judi, you just stop in Beijing and Guangzhou during your transit. For this reason, you are not qualified for 72 hours free transit. However, if your total transit is less than 24 hours, you still can avail 24 hours free transit. In this case, you just need to apply for a stay permit when you arrive in Beijing.

According to what I read, 72 hours is counted from 00:00 of next day.