Final answer:
Grace displays secure attachment by exploring her environment comfortably in the presence of her mother and a stranger, indicating she uses her mother as a secure base.
Step-by-step explanation:
Grace's behavior of playing well with toys and exploring her playroom when her mother is near, even in the presence of a stranger, is an example of secure attachment. This attachment style is characterized by children using the parent as a base from which to explore their environment and seeking comfort from the parent in times of stress. With secure attachment, the toddler prefers the parent over a stranger, which is in line with the child's behavior in the given scenario.