Which of the following rulers extended this empire to the boundaries labeled 1 and 4 on the map? moctezuma i pacal the great huayna capac ac kan

Assuming you are referring to the map I've attached below, the correct answer should be Huayuna Capac.
It says on the map that it is the Incan Empire. The only ruler of the Incan Empire among these people was Huayna Capac. Moctezuma I was an Aztec emperor, whereas Pacal the Great and Ac Kan were Mayan rulers. 

It can provide a social code to protect each citizen's future economical earnings. and then obviously defending the country from invading countries.