How can price of a commodity impact on the equillibrium price and quantity of another commodity?

The commodities have to be somehow related - the price of lead won't affect the price of oats, or at least we hope it won't.

There are a couple of ways this works.

First consider directly related commodities...we'll say diesel, heating oil and jet fuel. These are essentially the same product, but they go to different users and so are processed differently once the basic fuel is obtained. There's only a certain amount of this fuel, so if they want to make heating oil less expensive in the wintertime or jet fuel less expensive in summer they increase the prices of the other two fuels to discourage their use.

Next consider indirectly related commodities, such as diesel and wheat. It takes a LOT of diesel to produce wheat - you need diesel to plant, fertilize, harvest and transport it. If the price of diesel increases, the price of wheat also increases.