Final answer:
The process of focusing on the essential elements of a problem by removing non-essential details is called Abstraction. It differs from distillation, which is a physical process used in chemistry. Other terms such as agenda setting, demedicalization, and heuristic are related to policy, sociology, and problem-solving respectively.
Step-by-step explanation:
The phrase "carving away the unwanted reality from the bones of a problem" suggests a process where non-essential elements are removed to focus on the core issues. This process is best described by the option b) Abstraction. Abstraction involves reducing and clarifying a concept to its fundamental parts, allowing us to concentrate on relevant features while ignoring non-essential details. In contrast, 'distillation', while also a process of purification, specifically refers to a physical process used in chemistry to separate mixtures based on differences in volatilities.
As for the other questions, stage of public policy referred to in question 10 is a) agenda setting, where problems are identified for potential action. The removal of homosexuality from the DSM, mentioned in question 20, is an example of d) demedicalization, which means a condition is no longer classified as a medical disorder. Lastly, the mental shortcut used to solve problems provided in question 10 is b) a heuristic.