The given expression is:

$1 + 2y^6 - 4y^3 - 6y^6 + 4y^3 - y^5 - 9$

Let's simplify this step by step by combining like terms.

1. Combine the $y^6$ terms: $2y^6 - 6y^6 = -4y^6$
2. Combine the $y^3$ terms: $-4y^3 + 4y^3 = 0$
3. There is only one $y^5$ term: $-y^5$
4. Combine the constant terms: $1 - 9 = -8$

Now, the simplified expression is:

$-4y^6 - y^5 - 8$

Would you like more details on how I combined these terms, or do you have any specific questions?

Here are five related questions:

1. How do you factor a polynomial like the one above?
2. What are the steps to evaluate this polynomial for a given value of $y$?
3. How can you find the degree of a polynomial?
4. What does it mean to classify terms in a polynomial expression?
5. How do you differentiate or integrate this polynomial?

Tip: When simplifying expressions, always group like terms first to reduce complexity before moving forward with operations.