Can I connect an answering machine to the HP LaserJet Pro MFP M428/M429?

Yes, you can connect an answering machine by first removing the plug from the phone port, then disconnecting the answering machine phone cord from the phone jack and connecting it to the phone port on the printer. Then connect the phone cord that came with the printer to the fax port on the printer and to the telephone jack on the wall. (Page 4)