Download OSX Maverick and install onto formatted imac was 10.5.8, is that possible?

imac is running OSX 10.5.8, with 2.66Ghz intel core 2Duo and 4Gb ram.

I think to upgrade to the latest OSX which is Osx Mavericks, I have to get apple to send me a disc with Snow Leopard on it.

Install Snow Leopard, then install? Lion?
Then you can install Mavericks.

But If you can download Mavericks, can you just do a clean install on to the imac if you format the hard drive? Why do you need to go to all the hassle of goin through these stepping stones or different OSX's?

The correct procedure is to install Snow Leopard and then upgrade it with software update. After that you'll have access to the Mac App Store. You can download and install Mavericks for free. There is no need to install Lion or Mountain Lion. Mavericks will install over the top of Snow Leopard. However, it's always a good idea to make a backup first.

Since Mavericks is a free OS, if you have another Mac running Mavericks and have the ability to download it and create a USB installer - don't really see an issue of clean installing 10.9 onto any Mac that is capable of running it.

If you don't have another Mac with the ability to download 10.9, then you will need to get the 10.6 discs and upgrade your machine in order to gain that access to it. $20 is a cheap enough price to upgrade your Mac by 4 versions of the OS.

Personally, I would not try an upgrade install of 10.9 over 10.5 - only because I doubt even Apple has done that in their testing - unless you can find some reports of it working.