The correct answer is D) chain-nylon. The reason chain-nylon is the best anchor line for a small sailing vessel in rough weather is that it combines the strengths of both materials. The chain portion provides weight and stability to hold the anchor in place, while the nylon portion provides flexibility and shock absorption to withstand the strain of the vessel pitching and rolling in the waves. This combination helps to prevent the anchor from dragging or the line from breaking under the extreme conditions. The other options are less suitable - chain-wire would be too rigid, chain-manila would not have the same strength and durability, and an all-chain line would be too heavy and inflexible for a small sailing vessel.