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I beg to differ. The former means that the only two things you have are those two coats ("only" modifies "have"), but the latter simply means that you have two coats and not more of them ("only" modifies "two coats"). But anyway, I'm not sure how to express something like that in German.
Only I have two coats.
There may be other people with coats, but I am the sole person who has two coats.
I only have two coats.
I have nothing, except for two coats. But this construction also is used to mean ...
I have only two coats.
I have two coats. I have no more coats than that.
I have two coats only.
Same as immediately above.
I'm new to German so I may be mistaken, but I strongly suspect the German sentence, Ich habe nur zwei Mäntel, means the final two English sentences, above. It has been reported many times over the last several months, but it appears that no one is listening or refuses to believe what I know to be true. Or the German sentence really does mean that I have zero possessions except for two coats: no pants, no car, no hopes and dreams, no proverbial pot. Just the two coats.
According to Stack Exchange, English language users under "I only have vs I have only" the answer is as given above. I only have modifies the subject I, whereas I have only modifies the subject. The example dealt with friends with the later meaning that only a few of the acqaintances were friends. They referance http://www.wikihow.com/Use-the-Word-Only-Correctly. Hearing it either way means the same thing to me. I got it wrong also as my folks, although English language first people, grew up with English language second parents and in a German language community.