Final answer:
The mother is using the ego defense mechanism of regression.
Step-by-step explanation:
The ego defense mechanism that the mother is using in this situation is regression. Regression is when an individual reverts to a more immature behavior or stage to cope with anxiety or stress. In this case, the mother enters the boy's room offering him milk and cookies, which is a behavior more characteristic of nurturing a younger child. This can be seen as a way for the mother to alleviate her own guilt or frustration by temporarily becoming more nurturing and comforting.