try this first.
* For the printer instance in question, bring up the '''Printer properties''' dialogue.
* Select the '''Device settings''' tab.
* Ensure that the '''duplex unit''' is set to ''Installed'' rather than ''Not installed''.
You'll probably need to be logged in with administrator credentials in order to change the device settings.
im sure you may have read this but i guess it wont hurt.
how to duplex print
https://support.hp.com/us-en/product/HP-Photosmart-Premium-e-All-in-One-Printer-series---C310/4023238/model/4231204/document/c04402029/
And here is a link to a thread on this site that trouble shoots this issue.
[[HP Photosmart Premium e-All-in-One Printer - C310a Troubleshooting]]
Via HP
1. Verify the duplex-printing accessory has been installed properly. To verify this open the System Preferences and go to Print & Fax. Open the print queue of your printer. Click on Printer Setup and from the tab menu choose Driver. Verify the box next to HP Two-sided Printing Accessory (Duplexer) is checked.[br]
[br]
2. From the file used to print click the File menu and select Print.[br]
NOTE: The Print window might be minimized. Press on Show Details to show any available print option.[br]
[br]
3. In the expanded Print window you will find next to Copies the checkbox for Two-Sided. Check the box.[br]
NOTE: If the checkbox does not appear within the specific application print dialog, skip this step.[br]
[br]
4. To select the binding type click the lowest selection box listed as the name of the program (e.g. TextEdit)[br]
Will appear as Copies & Pages within Microsoft Office applications.[br]
[br]
5. Select Layout from the drop-down menu.[br]
[br]
6. Set the Two-Sided option as Long-Edge binding (Portrait), or Short-Edge binding (landscape).[br]
[br]
You may save the settings for future use by clicking Presets > Save Current Settings as Preset... Any used preset will remain default till another preset will be used.