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アリスが先生に田中にあれを見せてくれる
Let's assume this is in the third person point of view (I'm not included). Now how do I know, between Tanaka and The teacher, is the one that will be the target of the verb and the receiver of the favor?
Alice gives the favor of showing that to Tanaka for the teacher.(For teacher's sake)
Alice gives the favor of showing that to the Teacher for Tanaka.(For Tanaka's sake)
The scenario is that "Alice shows that to Tanaka, giving/doing a favor to the teacher."
Your sentence:
「アリスが先生{せんせい}に田中{たなか}にあれを見{み}せてくれる。」
has a problem in the 「先生に田中に」 part that is preventing the sentence from making perfect sense. Depending on your intended meaning, the 「くれる」 part would also need to be corrected.
If you wanted to say that Alice will show Tanaka something, which in turn will also benefit the teacher in some way, you could say:
「先生のために、アリスが田中にあれを（見せる or 見せてあげる）。」 or
「アリスが、先生のために田中にあれを（見せる or 見せてあげる）。」
Still, my sentences sound only 90% natural on the native level since they are based off of your original sentence. To make them sound completely natural, more information might be needed on exactly how this will benefit the teacher and/or what it is that Alice is showing Tanaka -- in other words, the whole story. It might even take two sentences to do it.
