Right off the bat, we can eliminate simple sentence; this sentence clearly has multiple subjects and predicates, separated by commas.
After I thought about it for a while, this is an example of a complex sentence. It isn't compound-complex, because to have a compound-complex sentence is to have two independent clauses, clauses that can stand on their own and make sense.
Breaking the sentence up, we have three parts: "As immigration patterns changed in the mid-1800s" (dependent clause), "most immigrants came from Germany to Ireland" (independent clause), "which are countries in western Europe" (dependent clause).
As can be seen, we have two dependent clauses but only one independent clause. So we can rule out compound sentence as well, since it also needs to have two independent clauses. So we are left with complex sentence.
This could technically be considered two complex sentences put together; the independent clause in the middle makes it so you could have just written "As immigration patterns changed in the mid-1800s, most immigrants came from Germany and Ireland." and it would make sense, or "Most immigrants came from Germany and Ireland, which are countries in western Europe" and it would also make sense.
Hope this helps!
