Multi-hop inference for explanation generation is to combine two or more facts to make an inference. The task focuses on generating explanations for elementary science questions. In the task, the relevance between the explanations and the QA pairs is of vital importance. To address the task, a three-step framework is proposed. Firstly, vector distance between two texts is utilized to recall the top-K relevant explanations for each question, reducing the calculation consumption. Then, a selection module is employed to choose those most relative facts in an autoregressive manner, giving a preliminary order for the retrieved facts. Thirdly, we adopt a re-ranking module to re-rank the retrieved candidate explanations with relevance between each fact and the QA pairs. Experimental results illustrate the effectiveness of the proposed framework with an improvement of 39.78% in NDCG over the official baseline.