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Usually if you have to place an item, you should be able to manipulate the location you have to place them. Much like opening a chest and taking an item or, placing an item back in, or on, is similar in that you drag the item from your inventory into the inventory window of the location.
After placing thing in the forge in chapter 1 or the anvil in chapter 3 you have to talk to the dwarf again and pay him for combining the items.
After that you can retrieve the finished item from the forge/anvil.