Answer:
The determiner that could be used before the noun house to refer to a specific house is "THE" as a definite article.
Step-by-step explanation:
"The" is one of the most common and well-known articles in English, it is an article that is used to refer to specific, unique or previously mentioned things which again makes them very special or specific, then if you use it with the word "house" you will be referring to a very special and unique house a very specific and well-known one.