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Nos is an object pronoun, it can be reflexive, direct or indirect, in this sentence, it is an indirect object, the verb mostrar is transitive, that means it requires a direct object, that would be su casa, that means she will show her house, now you have to answer: who is she showing it to? the answer is to us, so you have to use the indirect object nos. Remember that sometimes transitive verbs have implicit objects, so even if the object doesn't appear in the sentence, you still have to use the IOP. I'm not sure if this explanation is too vague, but I think it'll do for now.