Terlina III was the third planet in the Terlina system.
In 2338, following the destruction of the colony on Omicron Theta, Dr. Noonien Soong and his wife Juliana Soong fled to the forest of Terlina III and continued their work on androids. Juliana was critically injured in the escape. Before she died on Terlina III, her memories were transferred to a Soong-type android, who resembled her in appearance. The android Juliana eventually wearied of the solitude and left the planet. (TNG: "Inheritance")
In 2367, Soong summoned Data to Terlina III so that he could install the new emotion chip that he had developed. Unfortunately, his signal also summoned Lore, who stole the chip and murdered Soong. (TNG: "Brothers")
"tur-LEE-nah" was the pronunciation for this planet from the script pronunciation guide. [1]
"Brothers" did not identify Soong's planet by name; it was not called Terlina III until "Inheritance".
According to StarTrek.com, Terlina III was a M-class planet. [2](X)