Which parenting style seems to promote high-achieving children?

The correct answer is authoritative parenting.

Authoritative parenting refers to a parenting style characterized by high expectations and standards along with high levels of responsiveness. Authoritative parents set reasonable demands and high standards for their children. Additionally they are warm, supportive, responsive and trusting of their children, allowing their children to be autonomous within reason.

Authoritative parenting is the parenting style that seems to promote high-achieving children.

Authoritative parenting is characterized with demandingness and responsiveness.

Authorative parents have high expectations, demand their children to follow certain rules but at the same time, they are responsive enough and understand children's problems with that set of rules.