Final answer:
The device that manages network traffic and stores information about destinations in a network is a router, through its use of a routing table.
Step-by-step explanation:
The device that stores information about destinations in a network is a router. Routers are responsible for managing traffic within a network by directing data packets to their intended IP addresses. They achieve this through maintaining a specialized table known as a routing table, which contains the information necessary to forward a packet along the most efficient path to its destination.
Hubs, by contrast, merely rebroadcast all incoming data to every port. Modems convert digital signals to analog for transmission over telephone lines and do not manage network traffic. Finally, firewalls are security devices that monitor and control incoming and outgoing network traffic based on predetermined security rules, not for storing destination information.