Correct

代办 vs 代理

/ dàibàn vs dàilǐ /
Strokes

Definition

代办 as a Verb or a Noun, 代理 as a Verb, which means [to do sth.for sb.; charge d'affaires; to act on behalf of sb. on a responsible position].

Example

代办 and 代理 both are Verbs, which means "to do sth. for sb. else”.
1
fàngxīn
放心
  
,
zài
chūguó
出国
jiān
期间
  
,
zhè
jiàn
gōngzuò
工作
yóu
dàibàn
代办
  

Rest assured!I will do the job for you while you are abroad.

2
Lǎozhāng
老张
bìng
le
  
,
zhè
fèn
gōngwén
公文
qǐng
xiǎo
小李
dàibàn
代办
xià
  
!

Ask Xiao Li to deal with the document,for Lao Zhang is ill.

代理 is to do sth. officially for sb. else, that is, to be authorized to act for sb. else, such as in lawsuits, tax payment, commerce, etc.
3
Gāi
shāngdiàn
商店
tíng
停业
hòu
  
,
shànhòu
善后
shì
事宜
yóu
shī
律师
shìsuǒ
事务所
dài
代理
  

After the shop closed down, the law office was assigned to deal with its aftermath affairs.

4
men
我们
wěituō
委托
shǐguǎn
使馆
dài
代理
fāng
我方
de
qiānyuē
签约
shì
事宜
  

We commissioned the embassy to sign the contract on our behalf of us.

The object of 代办 (Verb) is business or work, while the object of 代理 (Verb) can also be the post.
5
xiānsheng
李先生
wěituō
委托
dàibàn
代办
shū
图书
yóugòu
邮购
shǒu
手续
  

Mr. Li asked him to buy the books by mail for him.

6
Zhāng
zhǎng
部长
bìngxiū
病休
jiān
期间
  
,
yóu
dài
代理
zhǎng
部长
  

He was in place of Minister Zhang during Zhang's illness.