The correct answer is D) stem the current and be falling aft very slowly when the anchor is dropped. When anchoring in a current, the easiest approach is to stem the current, meaning orient the vessel's bow into the current. This allows the anchor to set properly and prevents the vessel from swinging. Additionally, being slightly astern of the anchor drop point, or "falling aft very slowly," ensures the anchor line is not carried downstream by the current before it can take hold. This positioning allows the anchor to dig in and hold the vessel in place effectively. The other options are incorrect because A) stopping all headway could cause the vessel to be swept downstream before the anchor sets, B) making neither headway nor sternway does not account for the current's effects, and C) slow headway may not provide enough resistance to the current for the anchor to set properly.