Question

What dynasty lasted only two generations under the rule of shi huangdi?

Answer 1

The Qin dynasty lasted only two generations under the rule of shi huangdi.

The Qin dynasty was the first dynasty of Imperial China, protracting from 221 to 206 BC. It received its name for its heartland in Qin state (modern Gansu and Shaanxi), and was founded by Qin Shi Huang, the First Emperor of Qin.

Qin Shi Huang was also the first emperor of a unified China.

Answer 2

Its the Qin dynasty which had only two other emperors after shi huangdi 
hope this helps