Question

What city in the mongol empire was conquered four years after khanbalik (beijing) was conquered?

Answer 1

It should be Karakorum. The Mongol Empire had few cities. Karakorum was the largest in the area we call Mongolia. Most of the other cities were located within what is now China. 

Answer 2

Otrar-- located in central Asia, north of the Indian peninsula.

Genghis Khan organized and led the Mongols through an Asian conquest in the 13th century. After conquering China, the Mongols moved west taking over central and western Asia. The city of Otrar was conquered in 1219, four years after the conquest of what is now Beijing. The city held on in defense for months but eventually fell with the leadership surrendering.