Which of these enabled the incas to travel quickly throughout the empire to carry messages and warn the empire of an attack?

You are not putting any option but the correct answer is paved stone roads enabled the Incas to travel quickly throughout the empire to carry messages and warn the empire of an attack.

Communication was a crucial aspect of the Inca Empire. Many roads made of stone crossed the entire empire, thus allowing a wide communicative network. The main function of these roads was moving troops and goods. In addition to the roads, the bridges also had great importance, especially for crossing rivers.  

The communication was achieved through runners (young men called "chaskis") who were responsible for passing messages from one relay to the other. One chaski passed the message to the next in each relay. The messages could be verbal or through a quipu, a system that worked as a type of writing.  

herodotus taught this. herodotus was an ancient greek historian who was born in halicarnassus in the persian empire. he is known for having written the book the histories, a detailed record of his "inquiry" on the origins of the greco-persian wars.