Find the product

To find the product, we will use distributive law as follows:

$24 x^{2}(1-2 x)$

$=24 x^{2} \times 1-24 x^{2} \times 2 x$

$=24 x^{2}-48 x^{1+2}$

$=24 x^{2}-48 x^{3}$

Substituting  x = 3 in the result, we get:

$24 x^{2}-48 x^{3}$

$=24(3)^{2}-48(3)^{3}$

$=24 \times 9-48 \times 27$

$=216-1296$

$=-1080$

Thus, the product is $\left(24 x^{2}-48 x^{3}\right)$ and its value for $x=3$ is $(-1080)$.