A power-driven vessel with a 150-meter stern tow shall display __________.

In the context of navigation rules, a power-driven vessel that is towing another vessel must adhere to specific lighting requirements to ensure visibility and to indicate its status to other vessels. When a power-driven vessel is engaged in towing, especially with a significant length of tow, it is required to display a towing light above the sternlight.

This towing light is an important indicator that alerts surrounding vessels that the vessel is engaged in towing operations. It assists in maintaining safe navigation and helps prevent collisions, as other mariners can distinguish between a regular power-driven vessel and one that is towing. The sternlight alone would not provide enough information about the vessel's towing status.

The other options do not fulfill the specific requirements outlined for vessels engaged in towing. For instance, a single white masthead light or just two sidelights would not adequately convey the towing operation to other vessels. A flag indicating the nature of the tow is not a mandatory requirement under navigation rules; instead, the lights serve as the primary means of communication in terms of the vessel's operational status. Therefore, displaying a towing light above the sternlight is the correct action for a power-driven vessel with a 150-meter stern tow.