Simplify the sum of two polynomials.

1. Remove Parentheses: Since we are adding the two polynomials, we can remove the parentheses without changing the signs of the terms inside the second polynomial.
$$(-15n^2 + 5n + 8) + (-6n^2 + 8n - 4) = -15n^2 + 5n + 8 - 6n^2 + 8n - 4$$

2. Group Like Terms: Identify and group terms with the same variable and exponent.
$$(-15n^2 - 6n^2) + (5n + 8n) + (8 - 4)$$

3. Combine Like Terms: Add or subtract the coefficients of the like terms.
For the $n^2$ terms: $-15n^2 - 6n^2 = -21n^2$
For the $n$ terms: $5n + 8n = 13n$
For the constant terms: $8 - 4 = 4$

4. Write the Simplified Polynomial: Combine the results from the previous step to form the simplified polynomial.
$$-21n^2 + 13n + 4$$