Step 1 :The average rate of change of a function \(f(x)\) from \(x_{1}\) to \(x_{2}\) is given by the formula: \[\frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}\]
Step 2 :Substitute \(x_{1}=2\) and \(x_{2}=6\) into the function \(f(x)=-4x+2\) and then use the formula to calculate the average rate of change.
Step 3 :The function is a linear function with a slope of -4, so the average rate of change over any interval will be the same as the slope.
Step 4 :The average rate of change of \(f(x)\) from \(x_{1}=2\) to \(x_{2}=6\) is \(\boxed{-4}\).