All I can see is that if you add the 4&3 and takeaway from 12 you get the 5 and then if you add the 3&9 and takeaway the 16 you get the 4 but lost after that.
Just run this past the daughter (19) who has always been excellent at Maths (takes after her father you know). She says, if it is for a 6 year old, are we looking too deeply? Her answer would be 4
Add circles 4 + 3 + 5 gives you box 12
Add circles 3 + 9 + 4 gives you box 16
So just add
Circles 5 + 4 + ? to give you box 13