Predicting object locations in everyday scenarios is critical for service robots performing tasks such as object search and planning. Previous knowledge reasoning methods mostly use object class for prediction while neglecting n-ary multimodal properties. In this paper, we introduce a novel Few-shot n-Ary Knowledge Inference framework, FAKI, aimed to infer target locations using large language models (LLMs). By integrating few-shot In-Context Learning (ICL) method, we select the top-k most similar samples using K-Nearest Neighbors (KNN) for contextual information. To solve incomplete observations in few-shot scenarios, we provide the Metainfo, which contains data distribution in the trainset as hints for LLM. Leveraging KNN and Metainfo, our method achieves state-of-the-art (SOTA) performance on the LINK dataset for location prediction, outperforming the previous SOTA by 17.6%. Furthermore, we investigate the effects of prompt design, ICL, and top-k selection on prediction accuracy, providing deeper insights in few-shot n-ary knowledge inference.