Correct

损害 vs 损坏

/ sǔnhài vs sǔnhuài /
Strokes

Definition

损害 and 损坏 both are Verbs, which means [harm; damage; spoil].

Example

损害 is applied to abstract things.
Examples ① ② ③ are all about abstract things. 健康 is also more abstract (compared with 头部 (head), 手脚 (hands and feet), 心脏(heart), etc.) But occasionally one also sees 损害了肝脏, etc.
1
Zhè
jiàn
chǒuwén
丑闻
  
,
sǔnhài
损害
le
zhè
wèi
xiānsheng
先生
de
míng
名誉
  

The scandal spoiled the man's reputation.

2
men
我们
néng
zuò
sǔnhài
损害
gōngzhòng
公众
利益
de
shì
  

We cannot do something harmful to the good of the public.

3
Guò
过度
yǐnjiǔ
饮酒
yánzhòng
严重
sǔnhài
损害
le
de
shēn
身体
jiànkāng
健康
  

His excessive drinking spoilt his health.

损坏 is applied to concrete things.
Examples ① ② are all applied to concrete things, but 损坏 is more literary, usually applied to loss as a whole; as to the concrete things in colloquial language, 弄坏, 破坏 are used (e.g 别把电视弄坏了 Don't damage the TV set)).
4
Sǔnhuài
损坏
gōng
公物
yào
péicháng
赔偿
  

If you damaged the public property, you should pay for it.

5
Zhè
zuò
miào
古庙
bǎocún
保存
de
hěn
hǎo
  
,
sǔnhuài
损坏
de
fāng
地方
dōu
dào
得到
le
shí
及时
de
xiūshàn
修缮
  

The old temple keeps in good condition and the damaged parts have been repaired in time.

Related

损害损坏