10.4.4 was the very first Mac OS X that came on Intel Macs. PowerPC Macs could be updated up to Mac OS X 10.5.8.
October 26, 2007 was the last time a new Macs were sold with 10.4.11. Thus a 2009 iMac should not be able to even have 10.4 installed on it. So that's why Anamusic is likely confused. 10.5.6 was released December 15, 2008, after which time, all Macs were shipped with 10.5.6 or newer, and had to use the system specific 10.5. installer, or 10.6 or 10.6.3 retail installer up till 10.6's August 28, 2009 release.
Intel Macs that shipped with 10.4.x could only use their 10.4.x installer discs, and newer retail releases of 10.5, 10.6 to install Mac OS X. You could jump directly from 10.4.4 to 10.6.3 retail to 10.6.8.
To learn about jumping to 10.6, see this tip:
If your Apple menu -> About This Mac says you have a G4 or G5 processor, then you don't have an Intel processor, and it predates 2006.