As I Understand the HP Officejet 6600 won't print in color even after cleaning the printhead,
Don't worry as I'll be glad to help, however, to provide an accurate resolution, I need a few more details:
Did you check if it prints color using the copier as a standalone without the need of a computer?
(if it doesn't work either, it's a hardware failure and you may want to Contact HP for a hardware service)
If it prints fine on the copier, follow the below steps:
Step 1: Use genuine HP ink cartridges
HP recommends that you use genuine HP ink or toner supplies. HP cannot guarantee the quality or reliability of non-HP or refilled cartridges. If you do not use genuine HP cartridges, the steps in this document might not resolve the issue. To check the authenticity of your cartridges, go to hp.com/go/anticounterfeit.
Step 2: Check the estimated ink levels
Check the estimated ink levels. If an ink cartridge is empty, your printer can print for a period of time in either greyscale or composite black, depending on which ink cartridge is empty. If a color ink cartridge is empty, the printer prints in greyscale using black ink. If the black ink cartridge is empty, the printer prints in composite black using color ink. Composite black might not be as dark as regular printouts.
Step 3: Replace any low or empty ink cartridges
Replace any critically low or empty ink cartridges, and then try to print again. Skip this step if all ink cartridges show healthy ink levels.