Final answer:
The correct word to use in the sentence is 'my', making the sentence 'Your house is as big as my house.' 'My' is a possessive adjective used before a noun, in this context implying 'house' although it's not stated.
Step-by-step explanation:
In this sentence, the correct word to use is 'my'. So, the sentence reads, 'Your house is as big as my house.' The possessive adjective 'my' is used before a noun, which in this context, would be 'house' though it's not directly mentioned in the sentence. The word 'mine' is a possessive pronoun and is used in place of a noun, not before it, and 'I' and 'me' don't fit logically into this sentence.
Answer: mine
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