What command prevents a router from sending EIGRP messages out of an EIGRP-enabled interface?

The command that prevents a router from sending EIGRP messages out of an EIGRP-enabled interface is "passive-interface interface-id." When this command is configured on an interface, the router will not send EIGRP hello packets or updates on that interface, effectively making it passive. This is particularly useful in scenarios where you want to maintain the EIGRP routing information without allowing EIGRP routing traffic on certain interfaces, such as on a network with end hosts or volunteer providers.

This command helps in reducing unnecessary EIGRP traffic and can enhance security by preventing EIGRP from advertising routes on interfaces that connect to end-user devices. Additionally, it helps to prevent any EIGRP neighbors from forming on those interfaces, which might be desired in specific network designs where not every interface should participate in the EIGRP routing process.

The other choices do not represent valid or recognized commands in Cisco IOS for managing EIGRP communication.