The map showes the mongol empire at its height. which of the following regions had the most territory conquered by the mongol empire?

Since you provide no picture , In the past, mongols was able to conquer almost all part of Asia and some part of eastern Europe.

So here are some territories that mongols did not conquer :
- Western Europe, such as France and England
- South East Asia , such as malaysia , Indonesia, Thailand
- Africa , such as Egypt 

What’s the question here?