The trick to this question is to demonstrate that you not only persuaded others of a decision, but that it was the right decision.
As a data analyst intern at my last company, we didn’t really have a modern means of transferring files between coworkers. We used flash drives. It took some work, but eventually I convinced my manager to let me research file-sharing services that would work best for our team. We tried Google Drive and Dropbox, but eventually we settled on using Sharepoint drives because it integrated well with some of the software we were already using on a daily basis, especially Excel. It definitely improved productivity and minimized the wasted time searching for who had what files at what times.