Allowing passengers to ride on the __________ or __________ while underway is reckless operation.

The correct answer highlights the danger associated with allowing passengers to ride on the bow or gunwale of a vessel while it is underway. The bow is the front section of the boat, and the gunwale is the upper edge of the boat's side. Riding in these areas can create significant safety risks due to instability and the potential for falls overboard, especially when the boat is in motion or encounters waves.

Passengers standing or sitting on the bow may not have proper handholds or secure footing, which increases the likelihood of accidents. Similarly, the gunwale, being the upper edge of the side, does not provide a safety barrier to prevent individuals from falling into the water. Therefore, to ensure the safety of everyone on board, regulations prohibit such practices to minimize the risk of injury or drowning.

Other options refer to areas that may not present the same level of risk. While it’s important to follow all safety guidelines on a boat, the bow and gunwale specifically highlight areas where passengers would be at a higher risk due to the nature of their positioning while the boat is actively moving.