To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a+2b$ and $\left(a-2b\right)\left(a+2b\right)$ is $\left(a-2b\right)\left(a+2b\right)$. Multiply $\frac{2b}{a+2b}$ times $\frac{a-2b}{a-2b}$.
Since $\frac{2b\left(a-2b\right)}{\left(a-2b\right)\left(a+2b\right)}$ and $\frac{8b^{2}}{\left(a-2b\right)\left(a+2b\right)}$ have the same denominator, add them by adding their numerators.
