A power-driven vessel operating in restricted visibility must show __________.

In restricted visibility, a power-driven vessel is required to display all of her normal navigation lights. This is mandated to ensure that the vessel is visible to other vessels nearby, which is critical for safe navigation and collision avoidance. The display of normal navigation lights helps other mariners identify the type of vessel and its status, which is especially important when visibility is compromised due to fog, rain, or other atmospheric conditions.

The other options do not fulfill the legal and safety requirements for vessels operating in restricted visibility. For example, simply showing a foghorn or having a series of colored lights does not provide the comprehensive indication of the vessel's presence and characteristics that standard navigation lights do. In addition to displaying navigation lights, a power-driven vessel will also typically sound a fog signal, but that is a separate requirement from visual identification.