IPA: /ˈtʃɪə.fəli/
KK: /ˈtʃɪr.fəl.i/
In a way that shows happiness or joy.
She smiled cheerfully as she greeted her friends.
Cheerfully → It is formed from "cheer" (from Old French *chiere*, meaning face or countenance, which evolved to mean mood or spirit) and "-fully" (meaning in a manner full of). The word "cheerfully" means in a manner full of cheer or happiness.
Think of someone showing a happy 'face' ('cheer') and doing so 'fully' ('-fully') — that's why cheerfully means to act in a happy way.