The excerpt that includes an example of metonymy is:
“The work was hard, but worse was the constant cough he developed from the fine coal dust, the cold and dampness from the pits and mines.”
In this context, "the pits and mines" can be seen as metonymy because it refers to the coal mining industry and environment as a whole, using a specific aspect (the pits and mines) to represent the entire experience and hardships associated with coal mining.