Explanation:
Error-reporting messages are used in networking to notify users or network administrators about errors or issues that occur during data transmission. These messages help in troubleshooting and diagnosing the problem.

The given options are:

a) Destination unreachable: This error-reporting message is generated when a router or a host cannot establish a connection with the destination IP address. It is often used to indicate that the destination host is down, the network path is broken, or the firewall is blocking the connection.

b) Source quench: This error-reporting message is sent by routers to the source host to notify it to reduce the rate of data transmission. It is used to prevent congestion in the network by slowing down the traffic flow.

c) Router error: This is not a type of error-reporting message. It is incorrect to consider it as one because routers do not generate error messages. Routers perform the function of forwarding packets between networks and do not actively communicate error conditions to hosts.

d) Time exceeded: This error-reporting message is generated when a packet's time to live (TTL) value reaches zero. It is used to inform the sender that the packet took too long to reach its destination and was discarded by an intermediate router.

Conclusion:
The correct answer is option 'C' - Router error. Router error is not a type of error-reporting message because routers do not generate error messages. The other options, destination unreachable, source quench, and time exceeded, are valid error-reporting messages used in networking.