To help you with these polynomial operations, let's go over each polynomial and the operations indicated in the exercise. Here are the polynomials defined in your work:

1. $P(x) = 6x^5 + 4x^4 - 3x + 6$
2. $Q(x) = 7x^4 + 3x^2 - 2x^2 + 7$
3. $R(x) = 9x^5 - 5x^4 + 6x^3 - 2x + 8$

The indicated operations include sums, subtractions, and expressions combining these polynomials.

Let's break down the operations requested:

1. $P(x) + Q(x)$: Add the terms with the same degree in $P(x)$ and $Q(x)$.

2. $Q(x) + R(x)$: Add the terms with the same degree in $Q(x)$ and $R(x)$.

3. $P(x) + R(x)$: Add the terms with the same degree in $P(x)$ and $R(x)$.

4. $P(x) + Q(x) - R(x)$: First, add $P(x)$ and $Q(x)$, then subtract $R(x)$ from the result.

5. $P(x) - Q(x) + R(x)$: Subtract $Q(x)$ from $P(x)$, then add $R(x)$ to the result.

6. $Q(x) - R(x)$: Subtract the terms in $R(x)$ from the terms in $Q(x)$ with matching degrees.

I can proceed by calculating each of these polynomial operations step-by-step if you'd like. Let me know if you'd like a detailed breakdown of each calculation or if you have specific questions about one of these operations.

Here are some additional questions related to polynomial operations:

1. How do we determine the degree of the resulting polynomial after addition or subtraction?
2. What changes in the polynomial's coefficients when adding versus subtracting polynomials?
3. Can these operations affect the overall shape or graph of a polynomial?
4. How can we simplify expressions with like terms in polynomials before performing operations?
5. Why is it important to align terms by degree in polynomial addition and subtraction?

Tip: When adding or subtracting polynomials, always align terms by their degree to ensure accuracy in combining like terms.