To find the product of the two expressions \( (4x^3 + 2^2)(6x - 9) \), we first simplify the expression inside the first parentheses:
\[ 2^2 = 4 \]
So we have:
\[ (4x^3 + 4)(6x - 9) \]
Next, we can distribute each term in the first parentheses to each term in the second parentheses.
- Distributing \( 4x^3 \):
\[ 4x^3 \cdot 6x = 24x^4 \] \[ 4x^3 \cdot (-9) = -36x^3 \]
- Distributing \( 4 \):
\[ 4 \cdot 6x = 24x \] \[ 4 \cdot (-9) = -36 \]
Now we combine all these results:
\[ 24x^4 - 36x^3 + 24x - 36 \]
The final expression written in descending order of exponents is:
\[ \boxed{24x^4 - 36x^3 + 24x - 36} \]