Which of the following goals is most responsible for high population in prison?4 goals=retribution, deterrence, incapacitation, and rehabilitation
You could make a case for any of the four goals that you mention other than rehabilitation. High prison populations essentially make rehabilitation impossible. All of the others could be responsible for high prison populations. I would argue that deterrence is the most likely candidate.
Americans tend to feel that people who commit crimes should be punished harshly. They believe that such harsh punishments will make others afraid to commit crimes for fear of incurring those punishments. For this reason, we have laws such as "three strikes" laws and we have mandatory minimum sentences even for nonviolent drug crimes. This desire to instill fear in the hearts of potential criminals is the main cause of our high prison population.
However, you may want to look in your text book to see if its authors have a different view of the issue. This is really more of a subjective question and can have different answers.