Final answer:
Hannah has mastered the concept of object permanence, which means she understands that her mother continues to exist even when not visible. This is a key cognitive ability that indicates significant developmental progress in young children.
Step-by-step explanation:
The cognitive achievement that twenty-month-old Hannah has mastered is called object permanence. This concept is a critical milestone in the sensorimotor stage of a child's cognitive development, according to the work of Jean Piaget. Object permanence is the understanding that an object continues to exist even when it cannot be observed. Hannah demonstrates this by realizing that her mother still exists even when she is not in Hannah's view. Egocentrism, conservation, and animistic thinking are different cognitive concepts that relate to a child's developmental stages. However, in this case, object permanence is the correct answer as it describes the cognition of knowing objects remain consistent and exist even when they cannot be seen or interacted with.