Step 1: Understand the Context.
The phrase "died ___ hunger" refers to a cause of death. In English, when describing death caused by a specific condition or disease, the preposition "of" is typically used. For example:
"He died of hunger" means he died because of starvation.
Step 2: Analyze Each Option.
Option (1): of — Correct, as "died of hunger" is the standard expression to indicate death caused by starvation.
Option (2): from — Incorrect, as "from" is not commonly used in this context for death caused by a condition.
Option (3): by — Incorrect, as "by" is used to indicate the agent or cause of an action but is less common in this specific construction.
Option (4): with — Incorrect, as "with" does not convey the idea of causation in this context.
Step 3: Final Answer.
$$
(1) \mathbf{\text{of}}
$$