How can we decide to go under or through a beam with the air duct??

if the beam height is bigger than40 cm we make opening in the beam if its less than that we go under it.

Depends the beam size and their location. If you have say W10 and you want to have duct of8" then you are compromising most of the web area and the beam capacity weakens significantly.

It depends on the false ceiling and net architectural height  which drawings require .

Also according to the depth of beam ,  which should be enough to make hole on it.