Correct

摆 vs 搁 vs 放

/ bǎi vs gē vs fàng /
Strokes

Definition

摆, 搁 and 放 are all Verb, all the three words mean “place; put”.

Example

摆, 搁 and 放 all mean "to place sth. at a certain place".
1) 摆 stresses display, 搁 is comparatively colloquial and more popular in the north of China and 放 is both colloquial and literary.

2) In these two examples 摆 is most appropriate because potted flowers and handicrafts are specially for display. If the sense of display is not stressed, 搁 and 放 will also do.

3) If the meaning of display in ③ is stressed, 摆 can be used, otherwise 放 or 搁 will also do.

4) In example ④ 搁 will also do and is more appropriate because it means "to lay aside". 放 will also do. 摆 will not do because the sense of display is not meant in the sentence.
1
liǎng
pén
huā
bǎi
zài
chuāngqián
窗前
  

She placed two pot flowers in front of the window.

2
Jiàzi
架子
shàng
bǎi
le
xiē
一些
gōngpǐn
工艺品
  

Some handicrafts are displayed on the shelf.

3
Xīn
mǎi
de
shā
fàng
发放
  
(
  
/
bǎi
  
)
zài
nǎr  
哪儿
  
?

Where should we put the newly-bought sofa?

4
Zhèxiē
这些
qián
xiān
  
(
fàng
  
)
zài
yínháng
银行
  
,
yòng
shí
zài
  

You can deposit the money in the bank and withdraw it when needed.

5
zhá
hǎo
le
  
,
xiān
fàng
fàng
  
,
shāo
liáng
xiē
一些
zài
chī
  

After the fish is fried,cool it for a while,and then serve it.

搁 also means "to put aside".
In the examples, ⑥ and ⑦ 放 will also do, but 摆 will not do.
6
Zhège
这个
wèn
问题
máng
  
,
tiān
zàishuō
再说
  

The problem is not pressing now.You may put it aside for several days.

7
ge
那个
bàogào
报告
zài
nàr  
那儿
hǎoduō
好多
tiān
le
  

The report has been left to him for quite a few days.

搁 and 放 also mean "to add to".
8
Tāng
yào
fàng
  
(
  
)
xiē
jiāo
胡椒
  

You'd better put some pepper into the soup.

9
fēi
咖啡
fàng
  
(
  
)
táng
fàng
  
(
  
)
  
?

What coffee would you prefer: with sugar or not?