The problem asks to multiply two binomials: $(8p - t^2)$ and $(-3d - 4t^2)$. The final answer should be a polynomial.

1. Problem Description

The problem asks to multiply two binomials: $(8p - t^2)$ and $(-3d - 4t^2)$. The final answer should be a polynomial.

2. Solution Steps

We will use the distributive property (also known as FOIL) to multiply the two binomials:

$(a+b)(c+d) = ac + ad + bc + bd$

$(8p - t^2)(-3d - 4t^2) = (8p)(-3d) + (8p)(-4t^2) + (-t^2)(-3d) + (-t^2)(-4t^2)$

$= -24pd - 32pt^2 + 3dt^2 + 4t^4$

The terms are already in simplified form and there are no like terms to combine.

3. Final Answer

The final answer is $-24pd - 32pt^2 + 3dt^2 + 4t^4$.