Synchronizing Notes between Mac and iphone

The following has some information that may help. iCloud: Notes overview

Als see the following quote from the above link:

However, if you upgrade your iCloud Notes account on an iOS 9 device or a Mac with OS X v10.11:

Your notes on those devices and on iCloud.com aren’t kept up to date with notes on any of your devices with iOS 8.4.1 or earlier, OS X v10.10.5 or earlier, or Windows.

It should. However the signature in your original post states MacBook Pro with OS X 10.6.8 which is why I included the quote about older versions in my previous reply. You may want to reply with what version of OS X on your Mac and what version iOS on your iPhone that you are using if it isn't 10.6.8

Then the fact that you are running 10.10.5 and upgraded to the new Notes on your iPhone would be the problem.

Again, see the quote below. That and more information is in: iCloud: Notes overview

However, if you upgrade your iCloud Notes account on an iOS 9 device or a Mac with OS X v10.11:

Your notes on those devices and on iCloud.com aren’t kept up to date with notes on any of your devices with iOS 8.4.1 or earlier, OS X v10.10.5 or earlier, or Windows.