1. **State the problem:** Simplify the expression $$\frac{4}{y^2-4} + \frac{1}{y-2}$$. 2. **Identify the formula and rules:** Recognize that $y^2-4$ is a difference of squares, which factors as $$y^2-4 = (y-2)(y+2)$$. 3. **Rewrite the expression with factored denominator:** $$\frac{4}{(y-2)(y+2)} + \frac{1}{y-2}$$ 4. **Find a common denominator:** The common denominator is $(y-2)(y+2)$. 5. **Rewrite the second fraction to have the common denominator:** $$\frac{1}{y-2} = \frac{1 \cdot (y+2)}{(y-2)(y+2)} = \frac{y+2}{(y-2)(y+2)}$$ 6. **Add the fractions:** $$\frac{4}{(y-2)(y+2)} + \frac{y+2}{(y-2)(y+2)} = \frac{4 + y + 2}{(y-2)(y+2)} = \frac{y + 6}{(y-2)(y+2)}$$ 7. **Final simplified expression:** $$\boxed{\frac{y + 6}{(y-2)(y+2)}}$$ This is the simplified form of the original expression, valid for $y \neq 2$ and $y \neq -2$ to avoid division by zero.