Q:

what is difference using of "地" and "得"

I have been learning Mandarin since 6 months ago, but i have problem with my title, could you guys make me clear about the difference between them? 
if i have example of sentences like below is wrong:
很快地吃

but it i think if I make sentences like below right
她吃得很快

Because sometimes I was confused when I use "地" and "得" in above sentences, so please kindly help me. Thanks

A:

There are three confusing words in Chinese: "的", "地", and "得".
For "的", it is usually used to describe the words following it. The structure is adj. + 的 + noun, for example, 勤劳的妈妈.
For "地", it is usually used to describe the action following it. The structure is adv. + 地 + verb, for example, 积极地回答问题. So 很快地吃 is correct. In a whole sentence, it might be 他正在很快地吃苹果.
For "得", it is usually used to describe the action before itself. The structure is verb + 得 + adv., for example, 回答得很好, or 吃得很快.

A:

We tend to put some adverbials in front of the verb but others after the verb. It depends on many factors.
It's hard to come up with a reasonable explanation why we say:
 (！indicates an imperative sentence, 。 a declarative sentence, and ， an incomplete sentence.)
快吃！
快点吃！
吃快点！
吃得快。
吃得很快。
快吃。

but
*快地吃！
*吃快！
*吃快。
*快地吃。
*吃得快！

Sometimes both are used:
他伤心地哭着，
他哭得很伤心。

Apparently, 地 is preferred when the verb is long or followed by something else.
?他开心地笑。
他开心地笑着，
他开心地大笑，
他笑得很开心。
他积极地回答问题。
*他回答问题得很积极。
他回答问题很积极。
他回答问题回答得很积极。

I think the word that comes after the verb is usually the focus or new information. If you omit the adverbs,
?他笑。
?他回答问题。

do not sound like complete sentences, which means the adverbs probably contain important information. That's why we tend to place them at the end of a sentence. On the other hand,
吃！
她吃完了。
他回答了问题。

are complete sentences, so
快吃！
她很快(地)吃完了。
他积极地回答了问题。

I think 了 is what makes all the difference--it means a new event has happened, which by itself contains significant information. We may first use 了 to notify a new event, then use 得 to add some details.
她吃完了，而且吃得很快。
他回答了问题，而且回答得很积极。
*她吃完了，而且很快地吃。
*她吃完了，而且很快地吃了。
*他回答了问题，而且很积极地回答。
*他回答了问题，而且很积极地回答了。

Not all adverbs/adjectives can appear in both positions, and not all of them need 得 or 地. For example, 快 itself is an adverb.
他快吃完了。 = He almost finished eating -> He is eating.
快吃。 -- 快 is more like “hurry up” or “come on”
他轻轻地说，
他说得很轻。

