哥 is used in: 哥哥 (older brother), 帅哥 (handsome guy - casual address), 大哥 (big brother / boss). It can also be used as an affectionate term for older males who are not relatives. It appears in place names: 芝加哥 (Chicago), 墨西哥 (Mexico).
Top 可 supplies the sound (kě → gē, k/g alternation, also seen in 歌). The doubled 'can' image was later folk-read as 'the older one who can do twice as much', though the doubling is mostly phonetic emphasis. Filed under Kangxi #30 口 - the mouth radical embedded inside each 可.
Bottom 可 - pairs with the top to embody phonetic doubling. The radical 口 (mouth) sits inside each 可, anchoring 哥 under the mouth / speech category in dictionaries. The full character then reads as a stacked double-可 - visually balanced, phonetically emphatic.
Filed under radical 口 (kǒu, #30) by convention. 口 is not a separate component in 哥, so no strokes are highlighted.
