I have a 15.25oz Betty Crocker box mix. On the back it says to use it all with 1 cup of water, 1/2oil and 3 eggs and that makes two 8 in rounds or 24 cupcakes.
I don't know how much I need, please help.
I'll assume you want your 4" round cakes to be the same height as the two 8" rounds the box would make.
The area of two 8" rounds is 2*pi*4^2 = 32pi. The area of two 4" rounds is 8pi, or 1/4 as much area. So you only need 1/4 of the box, and 1/4 of the ingredients you'd add to it.
So, if you have a scale, you could measure 3.8oz of the cake mix, and otherwise you'll need to measure the whole thing by volume and take a quarter of it. Then you'll need 1/4 cup of water, 1/8 cup of oil, and... 3/4 of an egg, which you can probably round up to an egg. If you really want to be careful, you can also just beat an egg in a small bowl or measuring cup, and then spoon out 1/4 of it to leave 3/4 to use.
You need a quarter the amount of batter to fill two 4-inch cakes if the batter is sufficient for two 8-inch cakes... assuming you want the cakes to be the same depth.
This is problematic because it's difficult to split three eggs in quarters.
For simplicity, I'd make 1/3 of the batter to keep the percentages correct and then don't pour it all into the pans, or use all of the batter but know that they will be taller layers.
So, you would use:
If you want to do quarters, you could get away with it by using a medium egg (if you can find them) or by beating one large egg and using 3/4ths of it... though you'd probably be fine using the whole egg, really...