Method, way, manner, and means all have the meaning of "way, method".

Method: refers to a method of doing things or solving problems in an orderly manner. Often paired with with.

e.g. He invented a new method to teach English as a foreign language.

He invented a new method to teach English as a foreign language.

way: A common word that can refer to either a general way or method or a special way or method. Often paired with in.

e.g. I can't think of a better way tosolve this problem.

I can't think of a better way to solve this problem.

manner: refers to a special way of behaving. Often paired with in.

e.g. He has a pleasant manner, and finds it easy to make friends.

He has a pleasant manner, and finds it easy to make friends.

means: to achieve something A method, means or means adopted for a purpose or goal. Often paired with by.

e.g. Nowadays Internet is a popular means of communication.

Nowadays, the Internet is a popular means of communication.