Final answer:
The phrase is an example of a metaphor, illustrating that Katniss feels a significant burden, akin to a ton of coal being dropped on her.
Step-by-step explanation:
The sentence 'I remember how I promised Prim that I really would try to win and I feel like a ton of coal has dropped on me' is an example of metaphor. This figurative language suggests that Katniss is experiencing a heavy burden of responsibility. Unlike a simile, which would use 'like' or 'as' to make a comparison ('feels like a ton of coal'), a metaphor makes a direct comparison without such words, in this case equating the sudden weight of responsibility to coal being dropped on her.