Re: duct size question - can i exhaust a 6" duct out of a 4" hole?
I'm thinking it would .... as well it would reduce the CFM and put strain on the of the exhaust fan shortening it's life.
or is such a reduction going to create too much noise/pressure from the restriction.
Think of a funnel with it's wider mouth and the smaller spout .... it's the size of the spout that controls how much flow will occur.
Or ... blow through a straw and realize how much back pressure there is when reducing the opening on the other end.
The size of the duct has a finite capacity for CFM....
4 inch - approx. 100 CFM
5 inch - approx. 200 CFM
6 inch - approx. 300 CFM
The fan you are using is spec'ed at 150 CFM with a 6 inch duct.
With the description of a 3 or 4 foot run with no elbows this would be the ideal case where the fan would be running at or near capacity.
Now reducing the exhaust opening down to 4 inch which only has the capacity to pass 100 CFM would create back pressure and effectively reduce the exhausting down to at least 100 CFM ( probably less ). This back pressure would also put a strain on the fan motor since it's trying to move more air than is flowing .... so the motor will over work and wear out quicker.
I'm thinking of one of two other options ....
Down sizing the fan to the next model of 110 CFM using the 4 inch duct and with the short run without elbows would allow flow at or near the rated capacity. This would be around the same output as the method you propose and with less strain on the fan motor.
Using the proposed fan but with reduced to a 5 inch duct would allow for the CFM to be nearer to the capacity needed. This would still result in a back pressure on the fan but certainly more beneficial than reducing down to the 4 inch.
However .... if it's mandatory to need the 150 CFm you might try contacting the manufacturer to see what size of ducting would work as a compromise.
Side note ....
You mentioned this exhaust fan would be located in the basement.
Since the exhaust fan will be removing air you may have to consider a source for " make up " air to replace that which is being removed. This should be considered if there are heating and /or hot water heaters that use combustion.
The exhaust fans can create negative pressures affecting the exhausting of those combustion devices .... affecting the drafts for venting.
The negative pressure that can exist can prevent those combustion devices from operating if too much air is taken away for their firing or you could have back drafting in chimneys
Just a thought.
"" an ounce of perception -- a pound of obscure "