Final answer:
The correct command to propagate the default static route to all routers is 'ip route 0.0.0.0 0.0.0.0 [next-hop]'. Proper redistribution into dynamic routing protocols is also necessary for the route to propagate across the network.
Step-by-step explanation:
The command to propagate the default static route to all other routers is A) ip route 0.0.0.0 0.0.0.0 [next-hop]. When you apply this command on a router, it tells the router to send any packets with destinations not found in the routing table to the specified next-hop address. It is necessary to configure this on a router to ensure that packets with unknown destinations can be forwarded towards the default gateway, typically the next upstream device on the network.
After configuring the default static route, it may also be necessary to redistribute this route into dynamic routing protocols to ensure that it is propagated to other routers in the network. The method to do this varies based on the routing protocol used (such as OSPF, EIGRP, or BGP). For example, in OSPF, you would use the 'default-information originate' command to propagate the default route.