。
She turned her face away to hide her embarrassment.
Literal
She [topic-は] shyness [possessive-の] sign [object-を] hide [in order to-ために] face [object-を] turned-away.
恥じらいの色 ('the color/sign of shyness') is a literary expression — 色 here means 'sign/indication' rather than literal color, a usage common in literary Japanese (怒りの色, 悲しみの色). 隠すために ('in order to hide') marks the purpose. 顔をそむける ('to turn one's face away') uses the verb 背ける written here in its kun'yomi reading そむける — a vivid expression of physically averting one's face to conceal an emotion.