Edit
As pointed out by Kent, an iMac with a 2.16 Ghz Intel 2 Duo seems to be like an iMac (Late 2006) instead of an iMac (Mid 2007).
Technical Specs for iMac (Late 2006)
Technical Specs for iMac (Late 2007)
Therefore, you can only run Lion. Unfortunately, finding a legitimate copy of Lion could be a little tricky if you haven’t already purchased it. If you search for OS X Lion in the Mac App Store you’ll only find Mountain Lion, and Apple no longer sells an OS X Lion USB Thumb Drive (part number MD256Z/A) in its online store.
One of your options is to buy from Amazon or another online retailer.
Or, get Snow Leopard.
Original Post
You have to install Snow Leopard first and then Mountain Lion.
OS X Mountain Lion system requirements
To install Mountain Lion, you need one of these Macs:
**iMac (Mid 2007 or newer)** (Yours)
MacBook (Late 2008 Aluminum, or Early 2009 or newer)
MacBook Pro (Mid/Late 2007 or newer)
MacBook Air (Late 2008 or newer)
Mac mini (Early 2009 or newer)
Mac Pro (Early 2008 or newer)
Xserve (Early 2009)
Your Mac needs:
OS X v10.6.8 or OS X Lion already installed
2 GB or more of memory
8 GB or more of available space
Your model must have a 64-bit EFI boot ROM.
An easy way to tell if you are running a K64 kernel is to use the uname command-line program. The "x86_64" in the excerpt below means that we are running a 64-bit kernel. If the output showed "i386" instead, that would mean a 32-bit kernel.
uname -a Darwin... root:xnu-1456.1.25~1/RELEASE_X86_64 x86_64
Therefore, you need to upgrade to Snow Leopard first.
Other Things
AirDrop and AirPlay will not work on your computer.
Sources
http://support.apple.com/kb/HT5444
Alternate Way
It is possible, but not necessarily legal, to install Mountain Lion over Leopard.
You can look at this.
There are a couple different approaches you can take.
Approach 1 - Erase the newer iMac, reinstall 10.6.8 and use migration assistant to migrate your Time Machine data
With the newer iMac:
- Insert your Snow Leopard DVD (not the gray disc, a retail copy) and boot to it either by holding C while powering on or holding option while powering on and then selecting the 10.6 DVD.
- Select "Disk Utility" from the Utilities menu in the Snow Leopard installer
- Select the iMac's hard drive from the list on the left in Disk Utility, click on the "Erase" tab, type in a name for the hard drive (Macintosh HD?) and click erase.
- Once the hard drive is erased you can close Disk Utility and proceed with the installation of 10.6, following the on screen prompts.
- Once the installation is finished your newer iMac will boot to the normal welcome to OS X screen.
- I believe the third or fourth step in setting up the newly installed 10.6 will ask you if you want to transfer information from an existing Mac. Make sure your external Time Machine disk is connected and choose the "From a Time Machine Backup" option and follow the onscreen prompts.
- Once the migration is finished you should be able to login with your normal user account and your data should appear to be just as it was the last time your old Mac backed up.
Approach 2 - Clone your older iMac to the newer iMac
This requires that you have a firewire cable
With your older iMac:
- Download Carbon Copy Cloner on your older iMac
- Power on your newer iMac while holding T, you should eventually see the Firewire symbol (sort of looks like a Y) floating around it's screen
- Connect the two Macs together via a firewire cable, your newer iMac should appear as an external disk on your older iMac's desktop
- Open Disk Utility (/Applications/Utilities) on your older iMac
- Select the newer iMac's hard drive (should be an orange icon) from the list on the left in Disk Utility, click on the "Erase" tab, type in a name for the hard drive (Macintosh HD?) and click erase.
- Once the newer iMac's hard drive is erased you can open Carbon Copy Cloner
- Follow the on screen prompts in Carbon Copy Cloner to select your newer iMac's hard drive as the destination and then clone your older iMac's hard drive over to it.
- Once Carbon Copy Cloner is finished you should be able to boot your newer iMac and browse through to see all of your older iMac's data now in place.
Hopefully one of those options works and you're able to get that data migrated with little to no pain.
Best Answer
You will need to buy the Snow Leopard installation DVD from the UK Apple Store
I'm not sure why you just got a redemption code. If you look at this information page about older versions of OSX it says when you buy Snow Leopard you get a DVD, but if you buy Lion or Mountain Lion you get a redemption code. Are you sure you got Snow Leopard?