Yama said: "Through my favour Auddâlaki Âruni, thy father, will know thee, and be again towards thee as he was before. He shall sleep peacefully through the night, and free from anger, after having seen thee freed from the mouth of death."
In plain words: Yama grants the first wish. Nachiketas's father, also called Auddalaki Aruni, will know his son and love him as before. He will sleep peacefully, free of anger, once he sees his son come back alive from death.