How can one country's patent be valid in an other country..??

Question

For example, How can a EUROPEAN patent be valid in USA...?

Answer 1

It isn't. Each country has its own patent office, and for your invention to be protected in that country, you'll need to file a patent with that country's patent office.

Answer 2

It can't.  The inventor would have to timely file a U.S. Patent application and get through the patent application process and get a valid U.S. Patent in addition to the European patent.