adultness; maturity
Refers to the quality of being grown-up, responsible, or emotionally mature. Often used in negative expressions like 大人気ない (childish, immature).
His behavior is childish.
I want to try to act in a mature manner.
幼稚 describes childish, immature behavior or thinking, the direct opposite of the composed maturity implied by 大人気.
大人気 read おとなげ means 'adultness/maturity', while the identical kanji read だいにんき means 'very popular' — the reading changes the meaning entirely.
Standard kanji spelling. Note: this is read おとなげ, not だいにんき.
Alternate spelling using げ to clarify the reading and avoid confusion with 大人気 (だいにんき, 'great popularity').
Compound of 大人 (おとな, 'adult') and 気 (け, 'sign, feeling, spirit'). The 気 here indicates a quality or disposition.