one's assignment or area of responsibility; the task, class, or duty someone is in charge of.
私の受け持ちは小学校の3年生の算数クラスです。
My assignment is teaching third-grade elementary school math.
彼は新入社員の研修の受け持ちになった。
He became responsible for training the new employees.
このプロジェクトの受け持ちを変えてもらえますか？
Could you change who is in charge of this project?