The equivalent youth size of a woman's 6.5 size shoe is roughly 4.5 in the United States. The 4.5 is considered a size for big kids, and does not include toddlers or infants.
The way to convert a woman's or man's shoe size to a youth size is to know the size of the foot. A woman's 6.5 size shoe is roughly 9.1 inches. The closest youth sizes are a size 4, at 8.75 inches, or a 4.5, at 9 inches exactly. As the women's sizes become higher, it is tougher to convert to a youth size. For example, there is no direct conversion between a woman's size 8 and a youth's.