Adult sizes won't fit on children's clothes. You will have to do two designs. You can make one adult sized and then just shrink it down for the children's sizes. I don't know what kind of software you are using, but if it's any kind of graphic software you should be able to resize you work.
Are you trying to save money by not having two separate design sizes? I do men's and women's shirts and have to get two sets of screens for that even. I do 12.5 inches wide for men and 10 for the women shirts.
It would be a good idea to have a youth shirt and adult shirt in front of you. You can cut a paper rectangle to represent the maximum print size you want for the kids shirt. Then you can see how that rectangle looks on the adult shirt. It's likely to look very small though.
Also you have to make sure that you won't be making shirts for kids 12 and under. If you do make them for that age group you will have to make sure you're in compliance with that federal law that went into effect recently for anything made for children 12 and under.
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