English Translation
He spent a few months wandering around Europe.
I am thinking the verb here is durchstreifen. meaning o roam / wander in which case should it not be: “Er verbrachte einige Monate damit, Europa durchzustreifen”.
In this sentence it is not “durchstreifen”, just “streifen”, and “durch” is a regular preposition.
Thats’s why the word order is how it is.
That said, “durchstreifen” also exists, but it is not a separable verb. So then it becomes “…, Europa zu durchstreifen”. This is analogous to the famous “umfahren”, which is also inseparable when it means “to go around”.
Also note that “streifen” (in this sense) is intransitive, and “durchstreifen” is transitive.