Which theory of punishment hinges on the principle that a criminal will fear the pain of punishment more than desire the pleasure of committing the crime?
deterrence
rehabilitation
retribution
societal protection

Deterrence is correct.

Explanation:

According to a definition given by the Cambridge Dictionary, deter is "to prevent someone from doing something [...] by making it difficult for that person to do it or by threatening bad results if they do it." So, according to this, the bad result is the pain of punishment, which is considered a discourager for the potential criminal.