Final answer:
Option B). A router is a device that directs data across different networks, including the Internet, making it the correct answer to what piece of equipment directs information to transmit over the Internet.
Step-by-step explanation:
One kind of network hardware that guides data transmission over the Internet is called a router. A router is a device that is specifically used to route data between different networks, including the internet. A server is responsible for managing network resources, a firewall controls incoming and outgoing network traffic, and a switch connects devices within a network by processing and routing data at the data link layer of the OSI model. Therefore, Option B). Router is the right answer.