The Promise that Couldn't be Kept (守れなかった約束, Mamorenakatta Yakusoku) is chapter 236 of the Naruto manga.
Shikamaru points out to Tsunade that a medical-nin should have been assigned to the Sasuke Retrieval Team. She agrees, but says that being a medical-nin requires "something special". Shikamaru goes to visit Naruto in the hospital and gets confirmation that Sasuke would not come back to Konoha. Sakura overhears this but pretends not to, entering the room to see how Naruto is doing. Naruto apologizes for failing but she avoids the subject. He persists, saying that he will one day fulfil his promise of bringing Sasuke home. Seeing how much Naruto has gone through, Sakura leaves after telling him that he won't need to fulfil that promise by himself next time. Sakura goes to see Tsunade and asks to learn how to become a medical-nin. Seeing that Sakura has that "special something", the desire to avoid losing those one is close to, Tsunade accepts.