Forgot to attach picture… here it is. Thanks!

It sounds be pretty straightforward to install a rigid duct straight out the back wall there. They may need to cut an access hole in order to get the ducting placement right. Definitely use rigid duct of the correct diameter, with an exterior damper.

While the home builder (the OP may be an owner/builder) may not know as much as they should about ventilation, range and cooktop vent hoods and associated duct work are installed by mechanical contractors operating under a mechanical permit that is separate from the building permit to construct a home--at least here in Virginia. The builder relies on the expertise of the mechanical contractor to ensure ventilation systems function as intended and comply with applicable codes at a minimum (ideally with best practices.). In my experience, the vast majority of mechanical contractors focus on the "H" and "AC" components of HVAC and are pretty ignorant of ventilation requirements and best practices.

Thanks all…. I really appreciate it!

Drop the insert out of the hood. Investigate 90 degree transitions. Drill a hole at the right height to achieve the duct. Attach rigid duct and 90 to the insert, then thread the needle as you install. The other connections should be made from the exterior, as you will need a short section that terminates in a damper.

Note: Hoods like this are non serviceable once installed, which is why they are a bad idea. A hood needs a removable access panel in order to be serviceable, and to deal with the duct. That hood really should be rebuilt with a rmovable front panel.

They generally have a duct on the back of the vent that will extend out the exterior wall. Just a straight shot out. And a louvered vent is installed on the outside. Not a very hard job if you take the filters out you can probably see the vent.

A long drilling bit that can be used to drill threw the wall from a line scribed from the duct works well

@minardi that is what the j staller was suggesting. I’m trying to rethink design though… wish I knew this sooner. @aklogcabin our installer was concerned of not knowing exact measurements and fitting when the vent hood is up!

It's not a vent; it's an exhaust.

It is an exhaust vent

Thanks for the clarification on verbiage !