The formation of 不胜枚举 involves the negation 不 (not) combined with 胜 (to bear) forming 不胜, meaning 'cannot fully,' and 枚 (a classifier for small items) combined with 举 (to lift/enumerate) forming 枚举, meaning 'to enumerate item by item'; the entire phrase thus literally means 'cannot fully enumerate each item,' indicating something is too numerous to list exhaustively.