sorry, in this statement (How could SO corresponds) I meant SN not SO.

I understand your confusion, it is a little bit confusing on tackling these kinds of similarity problems, at least in my opinion xD

But the way how I look at it, because those two triangles are similar, their sides would happen to make up a proportional relationship. You could write the proportional relationship with the sides of the two triangles like so:

Base of Triangle SNO/ Leg of triangle SNO = Base of Triangle NOW/ Leg of triangle NOW

So, SN would be the base of triangle SNO and ON would represent the leg of that same triangle. Therefore, you could put them like this on the left side of the proportion: SN (triangle base)/ ON (triangle leg). Now, the key here is side ON represents the leg in triangle SNO and the base in triangle NOW. The leg in triangle NOW would be NW so the right side of the proportion would be ON(triangle base)/ NW (triangle leg). This is the proportion Khan Academy came up with, I hope this helps.