Make sure that you have prepared for the driver installation by following the below given instructions. 10/100 Base-TX is the requirement of the wired connection in HP Officejet 6600
You should have a network router, switch, or hub with available Ethernet ports and check whether your computer is connected to the router or switch or hub. If it not connected, connect the router and check whether you have made proper connections.
Do not use a standard telephone cable, instead use the Ethernet cable like the one given in figure. Use the Ethernet cable to connect the printer and follow the guidelines.
Turn on the printer and remove the plugs from the Ethernet port which is available on the rear of the printer. Connect the Ethernet cable to the printer port, and then connect the other end of the cable to an available port on the network router, switch, or hub.
Download the print driver to complete the wired connection by visiting the website 123.hp.com/oj6600. Type the printer model HP Officejet 6600 and follow the instructions that appear on the screen. Download HP Easy Start app or the app may automatically download based on your printer model.
Choose the printer connection type when you are prompted by the printer. Select the wired or Ethernet connection as we are moving towards the wired connection setup.
If the wired connection setup is successful and you need not continue with the remaining steps. If the download gets failed, continue to the hp.support.com and type your printer model. Check with the operating system compatibility and correct version of the operating system.
Click Download which is visible next to the printer full feature driver in the Driver-Product Installation Software and follow the instructions that appear on the screen. Follow the HP Download and Install Assistant or select Download only to save and run the driver file from your computer.
Choose a printer connection setup as wired and try printing a self test page or some thing to test the printer function and connectivity.