When the Messenger of Allah ﷺ wanted to perform the ritual bath after major impurity, he would begin with his hands and wash them. Then he would wash his private areas, pouring water over them, and once they were clean he would wipe his hands against a wall. After that he would proceed with the ablution and pour water over his head.
حدثنا عمرو بن علي الباهلي حدثنا محمد بن أبي عدي حدثني سعيد عن أبي معشر عن النخعي عن الأسود
كان رسول الله ﷺ إذا أراد أن يغتسل من الجنابة بدأ بكفيه فغسلهما ثم غسل مرافغه وأفاض عليه الماء فإذا أنقاهما أهوى بهما إلى حائط ثم يستقبل الوضوء ويفيض الماء على رأسه
Sourcing, its chain is daif. Ahmad reported it (6/171) from the hadith of Saeed bin Abu Aruba, through the same chain. He is a mudallis, and he narrated using "an," but parts of the hadith have many corroborating witnesses.