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I'm doing a project on a safety occurrence but I don't understand how the RPM of an engine is affected by the fuel mixture. How does a richer than normal mixture result in lower RPMs?

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I assume you are referring to a fixed pitch propeller because a constant speed propeller will always hold the same speed as the governor automatically changes the blade angle.

Just like any piston motor there is an optimal mixture. Richer or leaner results in lower power. Planes are set up to run rich at full rich mixture so leaning during cruise or descent will produce more optimal power which will affect rpm slightly in a fixed pitch application. Excess fuel displaces oxygen which decreases power flighty.

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