Thayer is holding her infant cousin and she smiles at the baby. The baby observes Thayer smiling and imitates the smile by smiling back. The baby most likely learned to smile in this situation based on

The baby most likely learned to smile in this situation based on "modeling".

Explanation:

A strategy applicable in certain cognitive-behavioral psychotherapy approaches in which the individual understands by replication alone, in absence of therapist's clear verbal input, and a generalized mechanism in which individuals function as models for others, demonstrating the activity to mimic others.

This method is the very widely explored in developmental psychology with respect to infants. Albert Bandura developed the fundamental of behavioral modification most famously in his simple experiment on the Bobo doll in 1961.