1. Firefox Sync doesn't work from one PC to another, the Sync server sits in the middle.
2. Sync works across all Operating Systems which the Firefox and the Sync service are compatible with - which is virtually everything except iOS and non-Android phones.
3. Did you set up Sync on both "devices"?
   

https://support.mozilla.com/en-US/kb/how-do-i-set-up-firefox-sync
https://support.mozilla.org/en-US/kb/how-do-i-set-up-firefox-sync#w_part-3-connect-your-other-device-to-your-sync-account

I read all the documentation at the beginning. I synced the origin pc to store the data on the server. When I enter the 12 char code on the "Pair a device" screen, I got nothing. So I was not sure if these differences were a problem. I was setting up the new pc and did not directly from step1 to step2 in the sync process. I will try it again with a new code.

Both devices need to be online at the same time if you want to pair a device with the (3x4) 12-character code and sync needs to be set up and working on at least one (desktop) computer to get a 12-character code via that computer and enter that code on the other device (computer) to pair that device.

Enter the account name (email address) and password and the 26-character Sync key manually to connect to an existing sync account instead of using the 12-character code to pair a device.

1. open "Tools > Options > Sync" or "Firefox > Set Up Sync"
2. click "Set Up Firefox Sync" to go to "Firefox Sync Setup"
3. click "I Have an Account" : Connect
4. click "I don't have the device with me" at the bottom to enter the account settings (email, password, sync key)

• https://support.mozilla.org/kb/how-do-i-manage-my-firefox-sync-account#w_where-can-i-find-my-recovery-key
• https://support.mozilla.org/kb/firefox-sync-troubleshooting-and-tips