Which of the following would most likely require the use of PPPoE?

The use of PPPoE (Point-to-Point Protocol over Ethernet) is most commonly associated with DSL (Digital Subscriber Line) services. PPPoE is a network protocol that encapsulates Point-to-Point Protocol frames inside the Ethernet frames, which allows for the establishment of a direct connection over the internet.

This method is frequently used in DSL connections because it enables service providers to manage multiple clients over a shared network while facilitating the authentication of users and the provision of different internet service plans. It combines the functionality of a point-to-point connection, such as authentication and encryption, with the efficiency of Ethernet, thus providing an effective way of connecting users to the internet over DSL.

While DSL services utilize PPPoE for these reasons, cable modems typically rely on a different mechanism called DHCP (Dynamic Host Configuration Protocol) for connection, which does not involve PPPoE. Fiber optic connections also do not usually require PPPoE, as they tend to use different protocols to deliver high-speed internet without the need for the overhead associated with PPPoE. A local area network (LAN) does not typically involve PPPoE either, as it is designed for internal device connectivity rather than internet access.