how do I upgrade my imac osx 10.4.11

Choose About this Mac from the Apple menu and check the processor.

If it's a PowerPC Mac, it's already running the newest OS it can.

If it's a Core Duo Mac, clickhere, install the DVD, and run Software Update.

If it's a Core 2 Duo or better Mac, upgrade it as if it was a Core Duo Mac, and once done, if desired, open the Mac App Store and try downloading El Capitan. If you get told that it's incompatible with your computer, go to the online Apple Store and order a download code for Lion 10.7.

Mac OS X 10.7 and newer don't support PowerPC software such as Microsoft Office 2004. If you upgrade the OS, back up the computer first.

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I would think that a 2006 iMac, even a PPC, could run at least 10.5.8. My 2002 Quicksilver can.

Note that any big jumps in OS may require you install more RAM on your computer. I would check on the feasibility of doing that before upgrading any higher than 10.6. You may also simply consider it not worth the trouble. If this truly is a 2006 machine it is unlikely you can go much farther than 10.7 and even that is reaching the end of its lifespan. You are better off spending your funds on a newer computer unless you are really good at keeping old things going and are very, very patient.

Note, upgrading a PowerPC Mac to 10.5 or later will get rid of Classic.