This is the 9956th most frequent Japanese word.
赤く
"赤く" means "red" or "reddishly" (adverbial form of "赤い," meaning "red").
赤く functions as an adverb here, describing the change in color of his face to red due to reaction or emotion.
彼は顔が恥ずかしさで赤くなった。
He became red-faced due to embarrassment.
赤く is used as an adverb modifying the verb なった (turned), describing the color change of the apple to indicate ripeness.
リンゴが熟して赤くなった。
The apple ripened and turned red.
赤く is used as an adverb to describe the way the sky is dyed, emphasizing the reddish color.