I've been told that the following two sentences are metonomic:-
Itís nothing like the America I remember.
My brother is an Einstein at maths.
but I've been seearching on the Internet to understand it more and when I read the following I'm confused:-
A figure of speech in which one word or phrase is substituted for another with which it is closely associated, as in the use of Washington for the United States government or of the sword for military power or crown in lands belonging to the crown.
Can anyone explain this to me?
Your second example is certainly metonymic: here 'Einstein' represents any unusually intelligent person.
I see nothing remotely metonymic about the first, however. I suggest you recheck your sources!