Use a vertical format to find the sum.
\[
(5 y+10)+\left(y^{2}-3 y-4\right)+\left(4 y^{2}+8 y-3\right)
\]

Step 1 ：Given the expressions (5y + 10), (y^2 - 3y - 4), and (4y^2 + 8y - 3), we are asked to find the sum.

Step 2 ：To do this, we need to combine like terms. Like terms are terms that have the same variable and exponent.

Step 3 ：In these expressions, the like terms are $y^2$, $y$, and the constants.

Step 4 ：Adding the $y^2$ terms together, we get $y^2 + 4y^2 = 5y^2$.

Step 5 ：Adding the $y$ terms together, we get $5y - 3y + 8y = 10y$.

Step 6 ：Adding the constants together, we get $10 - 4 - 3 = 3$.

Step 7 ：Combining all these like terms, we get the sum of the three expressions as $5y^2 + 10y + 3$.

Step 8 ：\(\boxed{5y^2 + 10y + 3}\) is the final answer.