Find the average rate of change of the function $f(x)=x^{2}+4 x$ from $x_{1}=2$ to $x_{2}=8$.

Step 1 ：We are given the function \(f(x)=x^{2}+4 x\) and we need to find the average rate of change from \(x_{1}=2\) to \(x_{2}=8\).

Step 2 ：The formula for the average rate of change of a function over an interval [a, b] is \(\frac{f(b) - f(a)}{b - a}\).

Step 3 ：Substitute \(x_{1}\) and \(x_{2}\) into the function to get \(f(x_{1})\) and \(f(x_{2})\).

Step 4 ：Substitute these values into the formula to find the average rate of change.

Step 5 ：The average rate of change of the function \(f(x)=x^{2}+4 x\) from \(x_{1}=2\) to \(x_{2}=8\) is 14.0.

Step 6 ：This means that for every unit increase in x, the function increases by 14.0 units on average over the interval from 2 to 8.

Step 7 ：Final Answer: The average rate of change of the function \(f(x)=x^{2}+4 x\) from \(x_{1}=2\) to \(x_{2}=8\) is \(\boxed{14.0}\).