How big is this hood? How many CFM does it need? Conversely, how many CFM does it claim to move? In any case, the duct has to be steel and not penetrated by structural wood elements. It has to be large enough in diameter to keep the airflow between 1000 and 2000 ft/min. Bends need to be gentle. What is on the other side of this wall?

Generally, a path upwards through the cabinet, attic, and roof is ideal for hot cooking plume removal. Sometimes, the house architecture thwarts best practice and then we have to compromise.

@kaseki This is a 30 in" hood (Kobe CHX2230SQB) 680 CFM. Not sure how much CFM it needs, I have a 30" gas stove. This is an exterior wall, the other side of the wall is the yard.

If this wood wasn't there, would rear venting be good? Or would going a bit upwards then a 90 turn be better? Not sure if this could go all the way to the attic since it's a room above the kitchen.

Thanks.

What I would probably do if I were intending to use this hood, is open the sheet rock and frame out a large enough hole for the duct at the duct position, carrying the stud load(s) around the duct. What size duct does the unit call for, 6-inch, 8-inch? When the duct is installed with a suitable cap outside, I would be sure I had a damper at the hood and preferably one outside, and then stuff insulation around the duct and any lacking areas in the wall. Then the sheetrock could be patched as required, and covered with the hood.

If going up and out seems to be better, which sacrifices some of the cabinet and is more difficult to do without removing the cabinets to get at the wall, then the same task would be performed higher up, but the present holes in the wall still need to be fixed, so it is a bigger job.

You shouldn't dump the hood exhaust onto a deck or area where one sits, and in this case, more attention to what routes might exist going up could be useful.

@kaseki Thank you! This has been helpful. I will try the first suggestion. The yard is a side yard so it should be ok.