There are 2 ways a password can be assigned to a backup, and only 2. The first is that you checked "Encrypt iPhone backups" at some time in the past, were prompted for a passcode, were prompted to re-enter the passcode. It could have been 2 years ago; iTunes remembers. The other is that your phone connects to a corporate MS Exchange account, and your Exchange administrator installed a security policy requiring passcodes on backups.
There is a slim possibility that the message is erroneous. Is "Encrypt Backup" checked on the Summary screen when you connect your iPhone and click on its name in iTunes? If it is not try rebooting your computer.
The only other way to find the passcode is to keep trying passcodes that you might have used. Instead or trying to restore the new phone just uncheck the "Encrypt Backup" checkbox and start guessing.
I said "only" but there is another way that sometimes works. Elcomsoft makes password cracking software for law enforcement purposes. They have a backup password cracker specifically for iPhone backups. It is not free, but there is a trial version that will give you the first 2 characters of the password if it can. Their FAQ says that if you have a really good password it may not be able to crack it in your lifetime, but weak passwords are a snap. You can help it by giving it a list of passwords that you commonly use. Note that this is the only backup password cracker that has any chance of working. There are several other products on the market that have generated many complaints.
