The word 大哥 is formed by directly combining two meaningful characters: 大 (dà), meaning "big" or "eldest", and 哥 (gē), meaning "older brother". This combination creates a single concept where the modifier 大 intensifies the core idea of 哥, resulting in a term that signifies not just any older brother, but specifically the "eldest brother" or, by respectful extension, a senior male figure who commands authority and respect akin to a familial leader.