Does the expression take the way signify that you take a particular route with a specific destination? The sentence I came up with is
He took the way to the stadium.
Is that correct?
I live in the US, and find this usage not out of the ordinary. I certainly do not agree that it is "never correct" as some of the UK commenters do.
I find "take the adjective way" normal - the easy way, the wrong way, the quick way, the pretty way - but not "take the way".
On the other hand, "make one's way" is common, but has a connotation of it being more than just a journey: an effort, or a great endeavour.