When two power-driven vessels are crossing, the vessel which has the other to starboard must keep out of the way if __________.

In situations where two power-driven vessels are crossing, the rules dictate that the vessel which has the other to starboard must keep out of the way if there is a risk of collision. This rule is grounded in the principle of ensuring safety and the prevention of maritime accidents. The rule recognizes that when assessing a crossing situation, if the action of one vessel poses a threat to the other, it is imperative for the vessel that has the other on its starboard side to give way. This helps to establish clear responsibilities for navigating vessels and promotes safer interactions on the water.

The other options, although they may present scenarios that affect navigation, do not directly address the primary regulations governing vessel interactions in crossing situations. For instance, overtaking involves a separate set of rules where the overtaking vessel is responsible for keeping out of the way, regardless of the position of the other vessel. Poor visibility does impact navigation but does not change the fundamental responsibility outlined in the crossing rule. Finally, whether a vessel is under sail doesn't directly relate to the obligations of power-driven vessels in the context of crossing. Therefore, the criterion of having a risk of collision is the central factor that necessitates one vessel to keep out of the way in this scenario.