The effective circular area of the offset box will be smaller than the duct, so it is a restriction one doesn't really want. Also, the transitions into and out of the box cause another pressure loss. How restrictive this is depends on just what air flow rate (CFM) the hood system is operating with.

What shape hole exists at the top of the hood box?

What blower is being used for this and what is its rating?

To the casual observer -- me -- it looks like this space was designed for a significantly larger hood. May we have a photo of the working area below the hood?

In any case, it would be best to have a HVAC company with a fabrication shop build an interface between the hood and the hole in the wall.

its definitely way too small for the hood, but the main issue is that the exhagust doesnt line up with the vent and this was the builders ”solution”. Its a 390 CFM vent but nooo way is it pushing that through. Its a GE UVC7300SLSS

So what goes under it into the counter space on top of the drawers? Is this intended for a 36-inch induction cooktop? [Very soon, I suspect, we will be discussing actual ventilation requirements that apply to cooking. Gird thy loins.]

Its a 36” natural gas range top

Then you need the largest insert that can fit in that space, with sufficient blower power to achieve ca. 90 CFM/square foot of entry aperture in operation.

I recommend that you spend part time for a week or so reading all the hood threads you can search out on this forum for expanded understanding of what requirements are needed to be met for successful cooking plume capture and containment. And make-up air (MUA) is also a topic to become familiar with.

Immediate references that should be reviewed:

• First dozen or so pages of https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf for understanding of what the conceptual baseline is that residential hoods are trying to emulate in less space with better aesthetics.
• https://bamasotan.us/range-exhaust-hood-faq/ for emphasis on air quality.
• Hood FAQs on this forum

How well does it function please?

Also the range top has a requirement for distance above it to combustibles that has to be met. Normally, that entire zone would be metal associated with an overlapping hood.

Oh good point. ill look that up

One more $10 elbow would eliminate that box.

Hahah yeah they tired but theres not enough room to make it work. It’s too tight if a turn. The more disappointing thing is the hvac inspector said that it doesnt break any codes so im stuck with it. How do i force my builder to fix it?

In any case, that insert is too small for a 36-inch cooktop.

And..., I hate to bring this up so often, but the required distance of the cooktop to combustibles in the wall direction has to be met, and I'm going to take a wild guess that the wall behind has wood studs. Some gas cooktops and ranges require either a 6 inch gap, or a riser (back guard), or a non combustible wall area (metal studs, etc.).

I don't believe you can't get round duct to fit and elimate that grease trap box.

Two things: 1. where's the damper; 2. since you are pulling 300cfm standard (390cfm "boost" mode) this model specifies an available UXDT86 - Duct Reducer (any 8" to 6" reducer is the same) - I can't tell from the pic but if it's 8" round you can use 6" round to gain a little space from the wall. Also, don't know what's on the other side of wall but the straight through the wall can be cut back some so the elbow connection is further into the wall. As far as the wall hole not being centered on the hood hole that is not a problem when you have 2 elbows.

The dampener is on the exterior