What is the method of stowing a line that involves making circular turns piled loosely on top of itself?

Coiling down is the method of stowing a line that involves making circular turns piled loosely on top of itself. This technique is essential in the maritime industry and in various applications where ropes or lines must be stored efficiently and without tangles. Coiling helps prevent kinks and maintains the line's integrity, making it ready for future use. The loose coil allows for easy retrieval and deployment, which is particularly useful in situations where quick access to the line is necessary.

Other methods such as figuring eight and hanking have distinct structures and purposes; they do not involve the same loose arrangement as coiling down. Figuring eight creates a specific knot that is useful for belaying and securing a line, while hanking typically describes securing a line in a loop, mounted on a hook or similar support. The serpentine method also differs, as it involves a winding technique that does not yield the loose, accessible storage that coiling down provides. Thus, coiling down stands out as the most appropriate answer for this particular method of stowing a line.