Mashup is an application that implements specific functions by integrating one or more web APIs, which are capable of providing services or data on the Internet, thus avoiding the behavior of repeatedly building wheels. With the number of web APIs on various platforms being vast, identifying the suitable web APIs for mashups has become a challenging problem for developers. In this case, researchers propose many methods to recommend available web APIs to mashup developers according to their requirements. Given that the high-order interactions between data are crucial for the recommendation tasks, this work proposes a novel web API recommendation method called R2API. R2API constructs a series of homogeneous hypergraphs from historical data and then utilizes multiple HGNNs (Hypergraph Neural Networks) to learn the vectors for nodes in the hypergraphs. HGNN excels in capturing the high-order interactions between data while effectively mitigating the over-smoothing problem. To reduce the impact of noise and atypical features in historical data and enhance the quality of node vectors, R2API adopts a multi-task joint training strategy to train all HGNNs simultaneously. Meanwhile, R2API assigns semantic vectors to nodes in the hypergraphs during HGNN training to further improve the quality of node vectors. When faced with a specific requirement, R2API identifies its related mashup nodes in the hypergraphs and learns the requirement vector based on the vectors of these nodes, so as to complete the work of web API recommendation. Experiments conducted on the ProgrammableWeb and GitHub datasets show that R2API achieves superior performance compared to baseline methods.