Knowing the objective might help a Houzz pro aim you in the right direction:

visual appeal? hide duct work or hide wiring or plumbing or install recessed lighting?

Yes. I need to hide an air duct box

Is there any way to avoid all the ductwork and the soffit in the kitchen? What is the duct for?

A carpenter will frame the soffit after the duct is installed and then face it with drywall, tape and sand the seams. Then the drywall can be primed and painted by you or whoever you hire to do the work.

I cannot hide the air duct. My kitchen designer made a mistake and did not check where the ductwork was. Now they recommend me to do the soffit but do it after the cabinets are installed. I am looking for a good carpenter who can do this type of job in Orange County, CA

There are different kinds of duct -- including duct board duct and sheet metal duct and flex duct. Some duct work can sweat if enclosed and is usually intended to be in the attic or below the floor where it needs no shield to hide it.

If it is a return vent, that would be less likely to sweat

I suggest you have a discussion with the heat and ac contractor that installed the duct -- or one you choose -- and see what kind of duct this is and IF this is duct that you can enclose with drywall .

It might be you would need to paint the duct black so it visually disappears as a shadow when it is covered by a vented shield such as a lattice wall in front of the duct above the cabinets to the ceiling -- or something else that enables sufficient air flow.

It may be that you could enclose metal duct if you first insulate it before you enclose it.

What kind of duct is this?

My late husband was a heat/ac pro . While I am certainly not a pro, I know enough to not use drywall to enclose duct work without first getting the input of a heat/ac pro and that the reason involves potential moisture issues -- you don't want to risk mold inside your soffit..

Thank you so much for your suggestions

Metal pipe duct, likely galvanized steel. It comes in different sizes for different purposes.

https://www.homedepot.com/p/Master-Flow-3-in-x-2-ft-Round-Metal-Duct-Pipe-BCP3X24/100129266

I know that the smallest can be used for dryer venting and that you can use three of them -- the smaller nesting inside the larger -- to create a triple wall "chimney" pipe.

Does this long horizontal pipe connect to your stove hood exhaust? IF so, unless you can filter/catch all the grease from frying at the hood ... if any grease goes beyond the hood into the pipe -- then that horizontal pipe could, potentially, end up with layers of a greasy film building up inside and that could create a potential problem.

If it is venting a dryer, then your filter would need to catch all the lint or it could, potentially, end up accumulating lint.

If this is a return air vent for your heat & ac, you might, consider putting filters at the grate so dust isn't pulled into the horizontal pipe to accumulate.

Again, you might want to talk with the contractor that installed it to understand how it is used and specifically ask if it can safely be enclosed in dry wall.

Yes. This pipe will be connected to my stove hood exhaust. Can I build a soffit to hide it and then cover with drywall? What would be an alternative to avoid layers of grease?

It may well be that an excellent filter in your stove hood that is frequently cleaned or changed as recommended by the manufacturer -- or more frequently -- could prevent any problem. I'm not sure what is available and not qualified to answer the question -- only have just enough second hand knowledge to ask it. You might check with your local fire department if the contractor that installed the pipe is long gone and/or clarify with your architect, if you're working with one, if what was done was what was intended.

Thank you very much fir your feedback. I will ask my HVAC people

Not sure the stove comes under the heading of Heating and Air Conditioning ... but most H&C companies have a guy that focuses on duct -- and they might well have put this up, too. Good luck with your build. Let us know how it turns out.

Here is the update. Soffit has been built