While it is generally possible to connect an overhead hood to a downdraft duct assembly, it is not recommended. Hot greasy and moist cooking effluent should be ducted upward. Further, VaH Magic Lung hoods lose performance when the duct path adds too much "resistance" (called pressure loss). They are also more sensitive relative to conventional blowers to make-up air pressure loss.

Is the range on an outside wall? Can the hood be ducted into an attic to the roof, or directly to the roof? Do you have combustion appliances taking air from a space that connects to the kitchen? Do your performance requirements include low noise?

Assume that we cannot read your minds or see by clairvoyance your architectural layout.

Read the first dozen or so pages of this tract to learn what residential hood systems are trying to accomplish without being actual commercial hood systems.

https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf

@Kochipri Did you try a search on this topic before posting? If not, try using the search box at the top of page while you wait for further responses.. It should turn turn up dozens of previous threads discussing questions about re-using downdraft ducting with a range hood.

Thank you!! There is a wall behind and it is a dining room. And we have bedroom upstairs too.

What is in the soffit, if anything, and does it run to an exterior wall?

It is still possible to duct up and out if the house. Down and out will be just as useless as it is now. And filthier.