These verb patterns are created through the use of gerunds. Gerunds are verbs that have been converted to nouns. This can be a difficult concept to understand at first.

Consider this sentence: Speaking is difficult. In this case, speaking is a gerund (noun). Korean has a similar system. 영어 말하기가 어려워요.
 

Korean can turn a verb in to a noun by adding the suffix, 동사 + 기.
Engilsh can turn a verb in to a noun using to gerund forms. "VERB + ing" or "to VERB"

So, how do we know which form is correct?

I like to swim (o)
I like swimming (o)

I enjoy to swim (x)
I enjoy swimming (o)

I try to swim (o)
I try swimming (x)

As you can see, the gerund form changes to fit different the main verb. Unfortunately, gerund formation rules are irregular for all main verbs.

So, we have to learn this way:

like + to VERB (o)

like + VERBing (o)

enjoy + to VERB (x)
enjoy + VERBing (o)

try + to VERB (o)
try + VERBing (x)

I hope this explanation helps you to understand a little better. 

Do you have the way about better remember verb pattern words?

I learned verb patterns.

The verb patterns grammar

Do not use '-to verb' as below words.
avoid, recommend, enjoy, appreciate,anticipate, admit, can't see, keep, consider, deny etc..

1) I enjoy to play game. (x)
2) I enjoy playing game. (o)

I just memorize the verb, but I think that there must be a better way to remember the verb patterns.
Why don't people use 'to verb' with verb pattern words? Why does the verb patterns exist?
I want to know the reason or cause.
Is it just natural or common grammar?
Is it easy on speaking English?
Is there no reason?

If I know the reason or cause, I memorize better than if I don't know anything.
Sadly, my memory is not good. ;)

I already ask the question.
but he just answer me that you can add 'doing' like that I enjoy doing or I admit doing.
and you don't say I admit to do.

I know I can't say "I admit to do" because English has verb patterns.
Why does he say add 'doing' is the way about better remember verb pattern words?
I'm Korean. so I have not a lot of experience in using English.

Please, can you explain the way and the reason?

Thank you for reading my question.

Dear Bulis

Unfortunately there is no MAGIC answer to your question.Some verbs take GERUND (-ing) some take INFINITIVE (to-verb) and some take both.Sometimes those that take both have the same meaning for example I like swimming,and I like to swim.Sometimes they have a different meaning such as I remember going and I remember to go.

Sometimes we can only use one form.There is no Reason or logic,it's just the way the language is built.So I suggest the best way is to find some songs you like with those phrases in them and that way it will be easier to remember which form to use.

I am sorry I cannot give you any magic rule because there isn't one

Good luck with your English studies.