Synching mail local folders

As mentioned, please turn on iCloud on both computers. If you are trying to make what you see on each of your computer's displays the same you have to do that manually, there is nothing that Apple makes that automates that other than Migration Assistant which isn't what you are looking for.

About the best I can think of is to locate the .plist file and then copy it to the other computer to see if that might work however that may also be risky. If you are not familiar with .plist files they are the settings files for apps. I was able to find the following via Google:

"plist located in the Home/Library/Preferences directory. Moving the file to the desktop and setting up your email accounts again or simply restoring com."

Ensure your mail account is an IMAP account and turn on iCloud on both Macs. That is all you need to do, if your don’t know if your account is IMAP contact your ISP.