Final answer:
Kublai Khan's most significant achievement was becoming the first foreign emperor to rule over China and establishing the Yuan Dynasty.
Step-by-step explanation:
After the death of Genghis Khan, his grandson Kublai Khan succeeded him as the ruler of the Mongol Empire.
Kublai Khan's most significant achievement was becoming the first foreign emperor to rule over China. He established the Yuan Dynasty and fully conquered the Song Dynasty in 1279, making him the ruler of all of China.
Kublai Khan's attempts to hold a unified Mongol Empire together were largely unsuccessful as the empire had already started to unravel and divide into four separate sections known as khanates. So, the correct answer is b. Becoming the first foreign emperor to rule over China.