To install Mavericks, you need one of these Macs:
iMac (Mid-2007 or later)
MacBook (13-inch Aluminum, Late 2008), (13-inch, Early 2009 or later)
MacBook Pro (13-inch, Mid-2009 or later),
MacBook Pro (15-inch or 17-inch, Mid/Late 2007 or later)
MacBook Air (Late 2008 or later)
Mac mini (Early 2009 or later)
Mac Pro (Early 2008 or later)
Xserve (Early 2009)
Your Mac also needs:
OS X Mountain Lion, Lion, or Snow Leopard v10.6.8 already installed
2 GB or more of memory
8 GB or more of available space
Yours is 2006 model!
Since you can not see the logic board ID, you have to open the computer and find the label.