Answer :
To find the product of
$$
(-2x-9y^2)(-4x-3),
$$
we multiply each term in the first factor by each term in the second factor:
1. Multiply the first term of the first factor, $-2x$, by the first term of the second factor, $-4x$:
$$
(-2x) \cdot (-4x)=8x^2.
$$
2. Multiply $-2x$ by the second term of the second factor, $-3$:
$$
(-2x) \cdot (-3)=6x.
$$
3. Multiply the second term of the first factor, $-9y^2$, by the first term of the second factor, $-4x$:
$$
(-9y^2) \cdot (-4x)=36xy^2.
$$
4. Multiply $-9y^2$ by $-3$, the second term of the second factor:
$$
(-9y^2) \cdot (-3)=27y^2.
$$
Now, combine all these results together:
$$
8x^2+6x+36xy^2+27y^2.
$$
Thus, the product is:
$$
\boxed{8x^2+6x+36xy^2+27y^2}.
$$
$$
(-2x-9y^2)(-4x-3),
$$
we multiply each term in the first factor by each term in the second factor:
1. Multiply the first term of the first factor, $-2x$, by the first term of the second factor, $-4x$:
$$
(-2x) \cdot (-4x)=8x^2.
$$
2. Multiply $-2x$ by the second term of the second factor, $-3$:
$$
(-2x) \cdot (-3)=6x.
$$
3. Multiply the second term of the first factor, $-9y^2$, by the first term of the second factor, $-4x$:
$$
(-9y^2) \cdot (-4x)=36xy^2.
$$
4. Multiply $-9y^2$ by $-3$, the second term of the second factor:
$$
(-9y^2) \cdot (-3)=27y^2.
$$
Now, combine all these results together:
$$
8x^2+6x+36xy^2+27y^2.
$$
Thus, the product is:
$$
\boxed{8x^2+6x+36xy^2+27y^2}.
$$
