Want to install 10.6.8 over 10.9.5

You have to first erase the partition on which Mavericks is installed before you can install Snow Leopard on it. If all you want is Snow Leopard then why install it separately on two partitions? Why not simply delete the Mavericks partition and extend the Snow Leopard partition to the drive's full size?

You can't unless you remove the bottom partition, then extend the top one. Only one OS will be preserved.

Use an external disk with 2 partitions.

CLone both internal partitions to the external disk partitions

Boot from the external

Reverse the cloning from the external to the internal partitions, putting Snow Leopard where you want it, and Mavericks where you want it.

SuperDuper will do a full clone for free.

Carbon Copy Cloner has a 1 month free demo where all features are enabled during the demo

Disk Utility -> Restore can also be used to clone.

Strongly suggest have yet another backup that you do not touch while doing cloning back to the internal just in case you get confused and clone in the wrong direction.

What I specified was swapping the contents of the 2 partitions.

1) Can I get all the applications from the first partition back onto the first partition without having to reinstall them one at a time?

You might be able to do this with Applications -> Utilities -> Migration Assistant, however, I am not in a position to test this theory.

If the applications are self-contained (do not have files stored in /Library/Application Support or other places on the disk, then you can just drag and drop them AS LONG AS the apps are compatible with that version of Mac OS X.

Carbon Copy Cloner can selectively pick (or exclude) files and folders, but you have to know what you need to select.

2) Can I avoid putting all the applications from the first partition onto the second partition?

The mention I outlined would make an exact copy of each partition. As I just mentioned, Carbon Copy Cloner can select or exclude files, but you have to know what files you want to exclude. NOTE: Many Mac OS X apps may be needed in support of other apps, so it would be unwise to not copy them and it would be unwise to try to use the other OS version of the app.

1) Copy all data from the user on the second partition onto an external drive.
2) Use the installation disk to install Snow Leopard on the second partition.

3) Upgrade to Mavericks on the first partition.

This should work.The only question is do you have applications/data on the first partition that you want on the second? When booted into the new Mavericks partition you will be able to copy files to the 2nd partition if you have them showing in Finder's Sidebar.

Mark your last post as solved, it might help others who are looking for answers.