Eric is using Sugar Sync with Microsoft Access, and every time it uploads his files to sync it, it gives them a longer and longer file name. Leo says it's doing this because Sugar Sync doesn't know which copy is the most recent and the one he wants, so it saves them all. It has to increase the file name of each one because there are naming conflicts otherwise.
Eric could get a hard drive and just carry that from computer to computer. The issue with using Microsoft's SkyDrive or Office 365 is that they don't support Access because they want to push their SQL Server software instead. The Chatroom says that GoToMyPC is another option so that the data is kept on one PC, but accessed from another.
If he's planning to copy the whole database over, it's really important he uses USB 3.0 because it's much faster. He'll also want to separate out the databases so he's not copying 20 GB each time.
(Disclaimer: GoToMyPC is a sponsor)