Multi-dimensional bunch-by-bunch (BbB) measurements are an efficient tool to research beam dynamics induced by wakefields in storage ring light sources, yet they can have data misplacement problems on high-speed acquisition boards. Hence, a data synchronization module (DSM) was designed to solve the issue of data misplacement. We analyzed different synchronization states in the DSM and conducted testing of the DSM on a field programmable gate array to evaluate its performance. Test results indicate the synchronized DSM data from multiple high-speed acquisition boards corresponds to the bucket number in the bunch filling pattern. We found that the resolution of the longitudinal phase in three-dimensional BbB measurements can be improved with DSM and propose a scheme for multi-dimensional BbB measurements. In this paper, we will detail the structure of DSM and its limitations.