Expressing "to hope" with 指望 and 盼望
Both verbs have the same meaning “to hope”, but they are used differently.
The verb 指望
The verb 指望 
expresses some expectations for another person.
For example, “we rely on your conscience”.
expresses some expectations for another person.
For example, “we rely on your conscience”. Pay attention
The verb 指望 is used in a spoken language.
Examples
他总是能指望她明智的忠告
He can always rely on her wise advice
tā zǒngshì néng zhǐwàng tā míngzhì de zhōnggào
你休想指望我相信那种事
You cannot expect me to believe in it
nǐ xiūxiǎng zhǐwàng wǒ xiāngxìn nà zhǒng shì
不要指望在几个月内就能学会一门外语
You shouldn’t count on the possibility of learning a language in a month
bú yào zhǐwàng zài jǐ ge yuè nèi jiù néng xuéhuì yì mén wàiyǔ
指望 as a noun
指望 can be a noun which means “hope”.
Examples
父母对孩子的指望不切实际
Parents pin unrealistic hopes on their children
fùmǔ duì háizi de zhǐwàng bú qiè shíjì
这件事还有指望
There is still hope for this
zhè jiàn shì hái yǒu zhǐwàng
The verb 盼望
The verb 盼望 expresses a desire that a person is wishes will happen. For example, “I hope he will come back soon”.
expresses a desire that a person is wishes will happen. For example, “I hope he will come back soon”. Pay attention
The verb 盼望 is used both in spoken and written language.
Examples
我们非常盼望能再见到你
We are looking forward to seeing you again
wǒmen fēicháng pànwàng néng zàijiàn dào nǐ
她盼望着和女儿通电话交谈
She was looking forward to talking on the phone with her daughter
tā pànwàng zhe hé nǚ'ér tōng diànhuà jiāotán
成千上万赤贫的农民急切盼望搬到城里去
Thousands of impoverished peasants are hoping to move to cities
chéng qiān shàng wàn chìpín de nóngmín jíqiè pànwàng bān dào chéng lǐ qù