2x squared plus x minus negative 6 over 2x squared plus 7x plus 6 times 2x squared minus negative 3x minus negative 20 over x squared minus negative 2x minus negative 8 simply 

Let's start by simplifying the given expression step by step.

### Given Expression:
\[
\frac{2x^2 + x - (-6)}{2x^2 + 7x + 6} \times \frac{2x^2 - (-3x) - (-20)}{x^2 - (-2x) - (-8)}
\]

### Step 1: Simplify each expression inside the numerators and denominators.
1. **Numerator 1: \(2x^2 + x - (-6)\)**
   \[
   2x^2 + x + 6
   \]

2. **Denominator 1: \(2x^2 + 7x + 6\)**
   This is already simplified.

3. **Numerator 2: \(2x^2 - (-3x) - (-20)\)**
   \[
   2x^2 + 3x + 20
   \]

4. **Denominator 2: \(x^2 - (-2x) - (-8)\)**
   \[
   x^2 + 2x + 8
   \]

### Step 2: Substitute the simplified expressions back into the original expression.
\[
\frac{2x^2 + x + 6}{2x^2 + 7x + 6} \times \frac{2x^2 + 3x + 20}{x^2 + 2x + 8}
\]

### Step 3: Check for any common factors or further simplifications.
- The fractions do not have common factors in the numerators and denominators, and nothing can be factored further.

### Final Simplified Expression:
The expression is already in its simplest form:
\[
\boxed{\frac{(2x^2 + x + 6)(2x^2 + 3x + 20)}{(2x^2 + 7x + 6)(x^2 + 2x + 8)}}
\]

Would you like details on any specific step or further clarification? Here are some related questions to consider:

1. How do you factor quadratic expressions?
2. What is the process to simplify expressions involving polynomials?
3. How can you identify if a quadratic expression is factorable?
4. How do you multiply rational expressions?
5. What are common mistakes to avoid when simplifying polynomial expressions?

**Tip:** When dealing with complex algebraic fractions, always simplify individual terms before multiplying or dividing them to avoid errors.

Learn how to simplify complex rational expressions involving polynomials step-by-step with detailed explanations. This problem covers algebraic concepts such as rational expressions and polynomials. Suitable for students in Grades 10-12.

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