When someone is "on his own", it means that he is doing something independently, without relying on help from anyone else. Synonyms for this phrase include "solo", "independently", "by oneself", "singly", and "autonomously". These words indicate that someone is in charge of their own actions and decisions, taking responsibility for their own success or failure. Other related phrases that could be used in place of "on his own" include "going it alone", "flying solo", "standing alone", and "self-sufficient". Regardless of the specific word choice, all of these phrases convey the idea that someone is navigating their way through a task or situation without assistance from others.