The answer is, depending on country.
In Germany, all children of any ages can buy anything with previous approval by the parents. From age 7 on products costing less than the monthly pocket money cna be bought with approval after buying, from age 14 on all products.
So, as a result, you might have a 4 year old child ordering something online, and have to honor the order (just as 4yos frequently are sent to fetch bread from the neighbourhood bakery).
Obviously, cultural values affect this heavily — while in Germany and Japan this is normal, in many areas of the US people below 16 are not expected to act on their own, or buy things, so it can be obviously different.