Approach and Method are two words that are often confused due to the appearing similarity in their meanings. Strictly speaking there is some difference between the two words. 看看他们有什么区别。

Approach refers to an act or means of coming near or approaching as in the expression ‘made an approach’. In the expression ‘needs a new approach’, the word ‘approach’ has the sense of ‘a way of dealing with a person or a thing’.
made an approach/  needs a new approach。
approach 有 处理一个人或一件事的方法。

A method on the other hand is a word meaning ‘a way’ or ‘a process’. It refers to the manner in which a work is executed. This is the main difference between approach and method. You approach a problem with a view to tackle it. On the other hand you resort to a method with a view to solving it.

In other words you can say that the word ‘approach’ is based on ‘tackling’ things whereas the word ‘method’ is based on solving problems.

approach是处理事， method是解决问题

You will fail to tackle problems if your approach is not good and effective. At the same time you will fail to solve the problems if your method is wrong or ineffective. This is the basic difference between approach and method. In some cases your approach may pave the way for the method to solve the problem. This concept is primarily used in business. An approach to a business problem will pave the way for the finding of a method to solve it. In other words the approach has to be good for the method to follow.

Approach is the cause whereas method is the effect. The approach to a bridge (method) has to be good for you to reach the other end of the river in a safe manner. These are the differences between the two concepts, namely approach and method.

打个比方，一包水泥要搬到楼上，what's your appoach?  扔上去。  太重了，你用什么方法扔？  what's your method?   用投石车扔。

approach 和method 多使用才能理解。