It will run Sierra, the latest version of OS X. See Basic Steps for Upgrading OS X. You will need to install Lion after Snow Leopard in order to upgrade to Sierra. Since you are now running Snow Leopard 10.6.8 see below:
Upgrading to Lion
You can purchase Lion at the Online Apple Store. The cost is $19.99 (as it was before) plus tax. It's a download. You will get an email containing a redemption code to use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.
Lion System Requirements
1. Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7,
or Xeon processor
2. 2GB of memory
3. OS X v10.6.6 or later (v10.6.8 recommended)
4. 7GB of available space
5. Some features require an Apple ID; terms apply.
Are my applications compatible? See App Compatibility Table - RoaringApps.
Upgrading to Sierra
You can upgrade to Sierra from Lion or later. Sierra can be downloaded from the Mac App Store for FREE.
To upgrade to Sierra you must have Lion or later installed. Download Sierra from the App Store. Sign in using your Apple ID. Sierra is free. The file is quite large, about 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
The official list of Macs compatible with macOS Sierra:
2010 or Later
MacBook Air
MacBook Pro
Mac mini
Mac Pro
Late 2009 or Later
MacBook
iMac
Also, see The MacOS Sierra Compatibility List
Are my applications compatible? See App Compatibility Table - RoaringApps.