Why is it said that "the red-faced Guan Gong fought in Changsha" and "the black-faced Zhang Fei"?

These are the lyrics of the song "Rapping Faces", which is about the faces of Peking Opera. Guan Yu has a red face and Zhang Fei has a black face. The color of their faces is on the one hand consistent with the skin color of the two men in folklore and Three Kingdoms novels (e.g., Guan Yu's "face is like a heavy jujube"), and on the other hand, it is also in line with the rule that the color of the face in Peking Opera face painting reflects the character's personality.

In Peking Opera face painting, the red face symbolizes loyalty, uprightness, and bloodiness, while the black face symbolizes strength and power, and rudeness.

"Guan Yu's Battle of Changsha" is a story about Liu Bei's attempt to take over the four southern counties of Jingzhou (Wuling, Changsha, Zuoling and Guiyang) at the end of the Eastern Han Dynasty, sending his general Guan Yu to attack Changsha County, killing Han Xuan, the governor of Changsha, and ultimately winning the battle. The Romance of the Three Kingdoms also depicts the story of Huang Zhong, a veteran general, and Wei Yan, a man with a backbone in the back of his head, who were collected during the battle of Changsha.