There seem to be two different questions, here.
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What is the purpose of the “eagle” helicopter (and who is using it?
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Are there Hinds (or other Warsaw Pact choppers) assisting in the current Iraqi war?
Given the Hungarian markings and the architecture of the buildings behind it in the photo (I agree with censored that those buildings are more likely European than Afghani), I would say that the photo is of some Hungarian public relations chopper. All the stuff about “American” or “Afghanistan” is simply pasted into the web page with no reason to believe that is has anything to do with the chopper. (Remember the “photo” of the shark leaping out of the water at the guy hanging from a ladder off a Blackhawk under the Golden Gate bridge, last year? The internet has turned altering and mislabeling photos into a cottage industry.)
I would think that several former Warsaw Pact countries who are part of the coalition have probably provided their own helicopters. These could be for relief or resupply or combat: they are participating (at various levels) in all aspects of the war. (Unlike Haliburton, Sikorsky and Bell probably can’t demand a piece of the action by insisting only their equipment is used.)