What kind of messages does a brouter handle?

A brouter, or bridge router, is a networking device that uniquely combines the functionalities of both a bridge and a router. It is specifically designed to handle data packets that require both bridging (which operates at the Data Link layer, allowing for communication within a local network) and routing (which operates at the Network layer, enabling the forwarding of packets between different networks).

This means that a brouter can efficiently manage traffic by deciding when to bridge (connecting devices within the same network to allow for smoother communication) and when to route (sending data to devices across different networks). Since networks can have a mix of traffic, being able to simultaneously handle both local (bridged) and external (routed) communications is a significant advantage for optimizing data flow.

The other options focus on messages in terms of their format or exclusivity. The choice indicating only digital or only analog signals does not encompass the broader capability of a brouter to process various forms of data packets in the context of networking. The mention of exclusive network messages does not accurately reflect the versatility of a brouter, which can manage both local and external communication needs. This unique capability is why the correct answer is that a brouter handles data packets that require both bridging and routing.