First, reboot your computer. Sometimes the request for a password is mistaken and rebooting will clear it. Then connect the phone and click on its name in iTunes. Is "Encrypt backup" checked? If it is then at some time in the past (and it could have been 6 years ago if you had an iPhone then) the box was checked and a password was entered. Or you have a corporate MS Exchange email account and your IT Administrator required that the backup be encrypted.
Either way you have to figure out the password. Try unchecking "encrypt backup". It will prompt for a password. Make an educated guess. It is a password that you have used at some time in the past. (Unchecking the box is a faster way of guessing than trying to restore.)
There is no other way to restore that backup, unless you have maintained iCloud backups. These do not require or allow passwords, because they are already encrypted with your Apple ID password.
If you are desperate there is a commercial product that can break SOME backup passwords if they are not too strong. Visit elcomsoft.com for more information. This tool is intended for law enforcement use, and is priced accordingly, however, they have a trial version that will give you the first two characters of the password.