Which type of OSPF area must not contain any ASBRs and must not receive Extern LSAs?

The choice for the type of OSPF area that must not contain any Autonomous System Boundary Routers (ASBRs) and must not receive External Link-State Advertisements (Extern LSAs) is a stub area.

A stub area is designed to reduce the amount of routing information that routers need to maintain. By disallowing ASBRs, stub areas ensure that no external routes are advertised, which simplifies the routing table and minimizes the overhead associated with external route advertisements. Routers within a stub area will only exchange intra-area routes and inter-area routes, which makes the OSPF routing protocol more efficient within that area.

By preventing Extern LSAs in the stub area, OSPF optimizes resource usage. This is especially beneficial in scenarios where external routes are not needed locally and helps maintain the integrity and simplicity of the routing topology within that area.

The other types of areas, such as not-so-stubby areas or totally stubby areas, allow for some level of external routing information, with totally stubby areas being a more restricted version allowing only a default route. Backbone areas can contain ASBRs and receive external LSAs as they are the core of the OSPF network, connecting all other area types.