Question: Perform the subtraction and simplify: $(9x^4 + 3x) - (14 - 6x)$
1. **State the problem:** We need to subtract the polynomial $(14 - 6x)$ from $(9x^4 + 3x)$ and simplify the result.
2. **Write the expression:**
$$ (9x^4 + 3x) - (14 - 6x) $$
3. **Distribute the minus sign to the second polynomial:**
$$ 9x^4 + 3x - 14 + 6x $$
4. **Combine like terms:**
The terms with $x$ are $3x$ and $6x$, so:
$$ 9x^4 + (3x + 6x) - 14 = 9x^4 + 9x - 14 $$
5. **Final simplified expression:**
$$ 9x^4 + 9x - 14 $$
This matches the first option given.
**Answer:** $9x^4 + 9x - 14$