In a coltish manner; in a way that is playful, frisky, or showing youthful awkwardness.
From 'coltish' + '-ly' (forming adverbs from adjectives), which comes from Old English '-lice' meaning 'in the manner of.' This creates the standard English pattern for turning adjectives into adverbs.
When you add '-ly' to an adjective, you're following a 1,000-year-old pattern in English that basically means 'in the way that this adjective describes'—so 'coltishly' means 'in a frisky way,' just like 'happily' means 'in a happy way.'
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