Differences between "Verb + Adj", "Adj + Verb", "Verb + 得 + Adj" and "Adj + 地 + Verb"?
I will suggest my ideas (probably there are some mistakes, so please point them out). For each case I believe there can be several possibilities.

Verb + Adj :

Adj is an adverb defining or restricting the meaning of the Verb. For example,

一个人会走快很多，但两个人好像更有趣。
Yīgèrén huì zǒu kuài hěnduō, dàn liǎng gè rén hǎoxiàng gèng yǒuqù.
One person walks a lot faster, but two people seem to be more interesting.

Here, 快很多 is an adverb that specifies a relevant characteristic of the verb to walk. The important idea is not to walk but to walk a lot faster.

The ... + Verb is the subject of the adjectival verb Adj. For example:

我们出去好。
Wǒmen chūqù hǎo.
It would be good if we go out.

Here, 我们出去 (we go out) is the subject of the adjectival verb 好 (is good).

The Adj is the direct object of the Verb. For example:

我觉得很惭愧。
Wǒ juédé hěn cánkuì.
I feel very embarassed.

Here, 很惭愧 (very embarassed) is the direct object of the verb 觉得 (to feel).



Adj + Verb:

If the Adj is an adverb of time, it signals the time of the action. Such is the case of 快 which can also mean soon. For example:

他快回来了。
Tā kuài huíláile.
He'll be back soon.


The Adj is actually a verb. For example:

我每天都努力学习.
Wǒ měitiān dū nǔlì xuéxí.
I study hard every day.

努力 is a verb meaning to make a great effort. So here we have Verb + Verb and 学习 is the direct object of the verb 努力: to make a great effort studying.

The Adj is placed in the topic position but the underlying structure is Verb + Adj. For example:

这道题很难解。
Zhè dào tí hěn nán jiě.
This problem is difficult to solve.

Here, 这道题很难 is the object + verb placed in the topic position. We can rearrange the sentence to its &quot;natural&quot; order:

解这道题很难。
Jiě zhè dào tí hěn nán.
It is difficult to solve this problem.

We see that actually 解这道题 (to solve this problem) is the subject of the adjectival verb 很难 (very difficult).



Verb + 得 + Adj: The adjective describes (instead of restricting) the manner or the result of the state of an action. For example:

他走得很慢。
Tā zǒu dé hěn màn.
He walks (in a manner) very slowly.


他教得累了。
Tā jiào de lèile.
He taught so much (to the result) that he is tired.


Adj + 地 + Verb: The Adj + 地 is an adverb that defines or restricts the manner in which the action is carried in a particular situation. Because of this, it can be used for commands. For example:

你快快地跑。
Nǐ kuài kuài dì pǎo.
Run quickly!