"our country finds itself confronted by conditions for which there is not precedent in the history of the world; our annual agricultural productions amount to billions of dollars in value, which must, within a few weeks or months, be exchanged for billions of dollars' worth of commodities consumed in their production; the existing currency supply is wholly inadequate to make this exchange; the results are falling prices, the formation of combines and rings, the impoverishment of the producing class."
—from the populist party platform, 1892 according to populists, how would the free coining of silver address the problems outlined in the party's platform?

Free coining of silver might address the problems, which are outlined in the party's platform, Populist party were made by farmers, in order to gain their position back in the country. They didn't get any profit, even many farmers were not able to feed their family. They created a party for farmers, They simply meant that producers (farmers) deserved a fair return for their labor.

Secondly, There were very less banks at that time in rural areas & money was scarce so banks charged very high interest rates. If silver coining would be free, then the wage of that industrial process would affect this agricultural portion of the country. If that would happen, populist party was not be able to fight anymore. That's why it would address the problems in the society at larger extent

Hope this helps!