可 as an adverb of degree
可 has several functions. Let's look at 可 as an adverb of degree.
Adverbs of degree (程度副词) are used to emphasize a feature of an object or the intensity of something: very, too, unbelievable.
Using 可 with adjectives
可 
is placed before adjectives to intensify their meaning. It is most often used in exclamatory sentences. In these sentences, 可 gives more emotional coloring.
is placed before adjectives to intensify their meaning. It is most often used in exclamatory sentences. In these sentences, 可 gives more emotional coloring. Pay attention
The modal particle 了 is often placed after an adjective.
is often placed after an adjective.Examples
这小孩可淘气了！
This child is so naughty!
zhè xiǎohái kě táoqì le
他的汉语水平可高了！
His Chinese is so good!
tā de hànyǔ shuǐpíng kě gāo le
可 is often placed before the adverb 真 .
.
Examples
他的脾气有的时候可真坏！
Sometimes his temper is really bad!
tā de píqì yǒu de shíhòu kě zhēn huài
每天都得晚下班可真讨厌
Leaving work late every day is so annoying
měi tiān dōu děi wǎn xiàbān kě zhēn tǎoyàn
Using 可 with verbs
When 可 is placed before verbs, it has the meaning "finally".
Pay attention
可 has the connotation of surprise. The speaker didn’t expect it.
Examples
你可回来了！
You're finally back!
nǐ kě huílái le
这个问题我可处理不了
I can't deal with this problem
zhè ge wèntí wǒ kě chǔlǐ bu liǎo
The negative adverbs 别 and 不 can be placed before a verb. In this case, 可 means "by no means", "not at all".
and 不 can be placed before a verb. In this case, 可 means "by no means", "not at all".
Examples
你可别让他知道
Don't let him know
nǐ kě bié ràng tā zhīdào
可别提了！
Don't even ask!
kě bié tí le
她可不能这样说！
She couldn't have said that!
tā kě bù néng zhèyàng shuō