介绍： Hi Paulo and thanks for your question.

嗨，保罗，感谢你的提问。
And, as well as answering your question,
在解答你的问题的同时，
I'm going to answer a similar one at the same time from Renato.
我也会同时为雷纳托回答一个类似的问题。
And the use of preposition is a topic that worries many of my students
关于介词...

介绍： Hi Paulo and thanks for your question.

嗨，保罗，感谢你的提问。
And, as well as answering your question,
在解答你的问题的同时，
I'm going to answer a similar one at the same time from Renato.
我也会同时为雷纳托回答一个类似的问题。
And the use of preposition is a topic that worries many of my students
关于介词的使用，这是一个困扰我许多学生的主题，
I know because I'm often asked for advice about which preposition to use where,
我对此有所了解，是因为我经常被问到，哪个介词应该用在哪里，
especially around the time that assignments are due in!
尤其是在任务就要到期的时间附近！
I do think that prepositions are one of the most difficult areas of English to master,
我认为，对于教师来说，介词是英语中最有难度的一个领域，
because there are so many prepositions and so many different combinations of verb and preposition that have to be memorised individually.
因为存在着许多介词，而且还有很多不同的动词和介词的组合需要单独记忆。
But let's begin with your first example Paulo, when we say Happy Birthday.
接下来就让我们从保罗的第一个例子开始，当我们说生日快乐的时候。
And when we use Happy Birthday we're using a set expression or a greeting like Happy Christmas, Happy New Year or Congratulations,
当我们使用Happy Birthday的时候，我们其实是在用一种表达方式或一种问候，比如圣诞节快乐、新年快乐或者恭喜，
and if you wanted to follow this expression with a pronoun,
如果你想要在这种表达方式上加一个代词，
you would have to use the preposition to with it - Happy Christmas to you! Happy Birthday to you!
那么你就要用一个介词来与之进行搭配--祝你圣诞节快乐！祝你生日快乐！
although it might be more common simply to use the greeting without a pronoun in speech.
不过在口语中，简单的不加代词的问候语其实更加常见。
In your second example Paulo, for is followed by a pronoun, you, and functions as a preposition showing the intended recipient:
在保罗你的第二个例子中，for后面跟着一个代词--you，其作为一个介词的功能，就是指示预定接收者。
The parcel is for Jenny. The flowers are for mother. Here is a gift for you.
这个包裹是给珍妮的。这些花是给妈妈的。这是一个给你的礼物。
So now to answer Renato's question.

现在来回答一下雷纳托的问题。
In the examples you give, Renato, I'd say that the first example, with the infinitive verb, is the better choice.
在雷纳托你给出的这些例子中，我要说，带有不定式动词的第一个例子是更好的选择。
You've only given me part of the sentence – an efficient method to solve my problem
你只给了我这个句子其中的一部分--一个解决我的问题的有效方法，
but the phrase suggests an outcome or the solution to a problem.
但是这个短语表达了一个问题的结果或解决方案。
Let's put this into a complete sentence by adding a verb:
让我们通过加上一个动词来将句子变完整：
I discovered an efficient method to solve my problem.
我发现了一个解决我的问题的有效方法。
In this case, the second verb always appears in the infinitive form because these are all examples of the infinitive showing purpose:
在这种情况中，第二个动词总是以不定式的形式出现，因为这些都是不定式表达目的的例子：
I watched television all day to relieve my boredom.
我看了一天的电视，来缓解我的无聊。
I made her a chocolate cake to make her feel better.
我给她做了一个巧克力蛋糕，来让她感觉舒服些。
He went into town to order his new computer.
他进城来订购他的新电脑。
In each of the examples above, there is an outcome or an intention which is reported by the to clause,
在上面的每个例子中，都有一个由to引导的从句，来表达的结果或者目的，
similar to the one in your own example, Renato.
它们都和你自己的例子类似，雷纳托。
Finally, to look at the last example, if I said Shall we go out to eat lunch?
最后，让我们来看一下最后一个例子，当我说Shall we go out to eat lunch?的时候，
the verb go out would be followed by a verb, wouldn't it?
go out这个动词后面会跟着另外一个动词，对吧？
However, in your own example, Renato – Let's go out for lunch
但是，雷纳托，在你自己的例子中：Let's go out for lunch
the verb is followed by a noun (lunch), so we have to use the preposition for in this expression!
其动词后面跟着的是一个名词（lunch），因此我们一定要在这种表达方式中使用介词for!
Well Paulo, thanks for your question and I hope that both the answers will be useful to you.
好了，保罗，感谢你的问题，我希望上面这些回答都会对你有用！