DIAGNOSIS The noise is from loose components vibrating against the cabinet. The most common source is the rear access panel or the copper refrigerant tubing lines.
FIX Unplug the unit. Remove the rear plastic cabinet panel (usually held by a few screws). Inspect where the copper tubing passes through the chassis. If it's touching metal, wedge a piece of foam or a rubber grommet between the tube and the chassis to dampen vibration. Tighten any loose screws securing the fan shroud or compressor mounting plate.
IF THAT DIDN'T WORK The noise could be from the compressor's internal mounting springs. This is a factory defect. If the unit is under warranty, contact Honeywell for a replacement. DIY repair is not advised.
HEADS UP Before opening the cabinet, ensure the unit is unplugged. Do not kink or bend the copper refrigerant lines. They are pressurized.