What is the rated air flow of the hood you have purchased? The air flow determines how large the duct should be. If you make it too small you won't get the rate air flow and it will be noisy.

What is the width of the minimum width of the rectangular duct? It appears the depth is the width of a wall stud which is about 3.5 inches. My first reaction is the duct is too constricted.

Thank you. You’re correct the minimum width of the rectangular duct is 3.5 inches. The hood has a 510 CFM.

That configuration is creating a lot of static pressure and I'd be surprised if a Monogram hood has a very strong blower to overcome it. The result is that you'll likely have very poor exhaust performance.

What kinds of cooking do you do? How Often? For how many people? What range will be under that? How old is your house? How important is good indoor air quality to you? How important is noise?

If you'll have an induction range that you'll boil water on once a week then you'll be fine, otherwise you may need to consider other options.

I have a 36” induction cooktop under the hood. The hood has a 510/8.0 CFM/sones rating. I do cook quite a lot. My existing fan was very noisy so I’m not too concerned about noise. My house was built in 2003 and there is just 2 of us.