Upgrading to the next OS fromOS 10.6.8

That's going to depend on your exact year/model of Mac.

Open the Mac App Store and try to download el Capitan if your Mac Supports it.

Upgrade to OS X El Capitan - Apple Support

From there you can try to update to Sierra if possible.

How to get macOS Sierra - Apple Support

If your Mac cannot support el Capitan, you will need to buy Lion from the Apple Online Store.

http://www.apple.com/shop/product/D6106Z/A/os-x-lion

So we know more about it...

At the Apple Icon at top left>About this Mac, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...

Hardware Overview:

Model Name: iMac

Model Identifier: iMac7,1

Processor Name: Intel Core 2 Duo

Processor Speed: 2.4 GHz

Number Of Processors: 1

Total Number Of Cores: 2

L2 Cache: 4 MB

Memory: 6 GB

Bus Speed: 800 MHz

Boot ROM Version: IM71.007A.B03

SMC Version (system): 1.21f4

Excerpted from Upgrading macOS without fear:

If you are still running OS X 10.6 "Snow Leopard",get El Capitan from the App Store, install it, then upgrade to Sierra.

Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.

Application Compatibility

Applications Compatibility (2)

El Capitan 10.11 Compatibility information

macOS Sierra 10.12: Compatible Apps

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.