Multiply the following polynomials and write the resulting polynomials in descending order.

To multiply the polynomials \( (2x - 7)(3x^2 + 7x - 8) \), we will use the distributive property (also known as the FOIL method for binomials).

1. **Multiply \( 2x \) by each term in the second polynomial:**
- \( 2x \cdot 3x^2 = 6x^3 \)
- \( 2x \cdot 7x = 14x^2 \)
- \( 2x \cdot (-8) = -16x \)

2. **Multiply \(-7\) by each term in the second polynomial:**
- \(-7 \cdot 3x^2 = -21x^2\)
- \(-7 \cdot 7x = -49x\)
- \(-7 \cdot (-8) = 56\)

3. **Now, combine all these results:**
- \( 6x^3 + 14x^2 - 16x - 21x^2 - 49x + 56 \)

4. **Combine like terms:**
- For \(x^2\): \(14x^2 - 21x^2 = -7x^2\)
- For \(x\): \(-16x - 49x = -65x\)

So the resulting polynomial is:
\[
6x^3 - 7x^2 - 65x + 56
\]

Now, to fill in the coefficient responses:

- The value of the coefficient of the \(x^3\) term is **6**.
- The value of the coefficient of the \(x^2\) term is **-7**.
- The value of the coefficient of the \(x\) term is **-65**.
- The value of the coefficient of the constant is **56**.

So the final answers are:

- Coefficient of \(x^3\): **6**
- Coefficient of \(x^2\): **-7**
- Coefficient of \(x\): **-65**
- Coefficient of constant: **56**