Don't do things that damage other people's reputations.
Tips
usage
损害 is more formal than 伤害 (shānghài). 损害 often collocates with abstract things: 利益 (interests), 健康 (health), 名誉 (reputation). 伤害 is more for hurting people/feelings.
usage
Compare: 损失 (sǔnshī) = loss/to lose (focuses on the loss itself), 损害 = to cause damage (focuses on the act of harming).
