Why are two-winged animals much more common than four-winged?
Note you are talking about two very distinct conditions

In vertebrates, 4 "wings" only evolves once in vertebrates (in early birds) and only one set function as wings the others "wings" are control surfaces for low speed stability, they generate insignificant amounts of lift. for large animals like vertebrates you can't fit two sets of functional wings on the same animal. Large wings need a lot of space to flap and you would need to make the torso longer to give enough room for a second set of flapping wings, which would add a lot of weight and defeat the benefits.  

In Insects four wings is the default, the groups with two wings got them by transforming one set of wings into something else useful. Wing covers in beetles ,which protect wings from damage, and Halteres in flies which act as a sort of sensory organ to determine position. Two wings are more common numerically becasue those two groups are extremely successful. Basically if you have two of something but one will also work and evolution can turn the other set into something useful then you have a chance to lose one set of that thing. Two wings are more common numerically becasue those two groups are extremely successful. By turning four wings into two those groups ended up with more abilities than their four winged relatives, becasue they did not just lose the wings they turned them into something else.  

In insects wings actually evolved from gill covers, insects could have had six wings, why the first set never evolved would be an interesting question. It may be due how HOX genes are expressed in insect segments. 

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