There are several synonyms that can be used instead of "in the adjacent house." Some of these include "next door," "neighboring," "adjoining," "bordering," "contiguous," "nearby," or "proximate." All of these synonyms convey the idea of being close or connected to a particular location or structure. Using these different synonyms can provide variety in your writing and help to avoid repetition. It is essential to choose the appropriate synonym based on the context and tone of your writing to ensure that the intended meaning is conveyed clearly and effectively.