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You are already on the latest Safari that your Mac OS X can support now. To upgrade to latest Safari, you need to upgrade the OS X 10.6.8 to latest version. The latest OS X is 10.11 El Capitan. Upgrading to El Capitan also update Safari.
Follow the steps below to upgrade the OS X if your Mac support it.
Click on the Apple icon and App Store. This will bring App Store. Click Updates tab. If your Mac can handle latest OS X, then you will see Mac OS X El Capitan there with FREE UPGRADE button. Click Free Upgarde and enter your Apple ID and password.
This will download the update. It may take a few hours to download. Once the download is completed, it will bring the OS X Installer. Follow the onscreen instructions to install it. It may take up to 3 hours to install the upgrade.
If you have any difficult on following the steps above, please let me know.