Teruzuki was an Akizuki-class destroyer, built to fight aircraft. Mitsubishi launched her at Nagasaki on 21 November 1941 and completed her on 31 August 1942. The picture is not a photograph of her. It is a U.S. Navy recognition sheet of the class, ONI 41-42, from March 1943. The sheet calls the class Terutsuki.
On the night of 13 November 1942 she was in Abe's screen off Guadalcanal, with the battleships Hiei and Kirishima. Ships were sunk on both sides that night. Those losses are not credited to her. She was not sunk.
Two nights later Washington's 16-inch guns wrecked Kirishima, and Kirishima capsized. Teruzuki was one of the destroyers that took off Kirishima's survivors. She was not sunk that night.
Early on 12 December 1942 she was Rear Admiral Raizo Tanaka's flagship on a supply run, off Savo Island. American PT boats hit her stern with two torpedoes. She lost her rudder and a propeller shaft. The fire reached her depth charges and she sank. Nine men were killed. Tanaka was taken off. Historians do not agree which boats fired. The usual names are PT-37 and PT-40. The hit is not pinned to one boat.