Animism, or the belief that objects are alive and have personalities, is a common childhood belief, which was extensively studied by Jean Piaget. Piaget attributed animism to a failure of the child to distinguish its own interior world from its exterior world.

It has been observed that as humans age some abilities decline while others improve. Researches have noted that over time crystallized intelligence tends to remain stable—or even increase.

Bobby is unable to demonstrate conservation, or the understanding that quantity does not change just because appearance does. This concept develops during the concrete operational stage of development. The preoperational stage is characterized by the inability to conserve, egocentrism, animism, pretend play, and use of symbols; therefore, Bobby is in the preoperational stage. Note that while the question describes conservation, this is not the name of one of Piaget's stages. 

Jean Piaget introduced the four stages of cognitive development: Sensorimotor, preoperational, concrete operational, and formal operational. Piaget was most concerned with the cognitive development of children that included abilities such as conservation and abstract thought. Erikson studied psychosocial development across the entire lifespan, Freud studied psychosexual development from birth to adolescence; and Thomas along with his colleague Stella Chess studied temperament, a precursor to personality.

Assimilation and accommodation both have to do with schemas and cognitive development. Assimilation is a process through which new information is incorporated into an existing schema. Accommodation occurs when an individual's schema is altered to fit new information. Therefore, in this case, the child has accommodated their existing schema to fit new information (that there are other names besides "cat" for furry four legged creatures). Sublimation is a defense mechanism coined by Freud and centration is the tendency for children to focus on one aspect of a problem even when two or more aspects may be relevant.

Gardner's "logical-mathematical" intelligence, the correct response, refers to the ability to analyze problems, solve mathematical equations, detect patterns, and think logically. Multiple theories of intelligence have been developed within the field of Intelligence Development.  Howard Gardner is one of these theorists. He provides a seven-faceted model of intelligence that includes the types listed in the response choices. "Linguistic" is incorrect as it refers to the individual’s command of language. "Spatial" is incorrect because it refers to the individual’s ability to manipulate and work with physical objects. "Interpersonal" is also incorrect because it captures one’s ability to successfully navigate social interactions and relationships. 

During early childhood (age 2 to 6 years) the child begins to engage in social interaction. He or she wants to be the center of attention. By encouraging the child to respect boundaries and providing discipline to control impulsive behavior, the child will learn a responsible way of living. 

Adolescence (age 12 to 18 years) is a time of identity crisis. At this stage, the child asks, "Who am I?" If the child can integrate values learned during previous childhood stages (trust, independence, impulse control, and intellectual curiosity), then they will have a strong identity and readiness to be an adult. If not, confusion can occur and they will be unable to make decisions about their role in life. 

The regressed behaviors of this client are characteristic of the “trust vs. mistrust” stage. When a child experiences trauma or neglect during this stage they are unable to develop a secure sense of trust with himself or herself or their caregiver. This leaves them feeling either excessively dependent or excessively detached. The client also demonstrates early development behaviors such as thumb sucking, which are indicative of an emotional age of about 1 year old in Erickson's model. 

The "industry vs. inferiority" stage most often occurs between the ages of 6 and puberty. It involves learning to master one's skills in order to develop a sense of competence. "Trust vs. mistrust" is the first stage that occurs during infancy, with the goal being to develop a sense of trust in the caregiver. The second stage is "autonomy vs. shame and doubt," which occurs between 1 and 3 years of age and involves developing a sense of independence. "Initiative vs. guilt" is the third stage, which occurs from ages 3 to 6 and involves assuming responsibility. "Integrity vs. despair" is the final stage of development and involves reflecting on one's life.