The simplified expression is \(12ac(4a + b) - 2bd(3c - d)\).
To simplify the expression \((4a + b)(a - 2b)(3c - d)\), you can use the distributive property and multiply the factors:
\[
\begin{align*}
&(4a + b)(a - 2b)(3c - d) \\
&= (4a + b) \cdot (a - 2b) \cdot (3c - d) \\
&= (4a \cdot a \cdot 3c) + (4a \cdot a \cdot (-d)) + (b \cdot a \cdot 3c) + (b \cdot a \cdot (-d)) \\
&\quad + (4a \cdot (-2b) \cdot 3c) + (4a \cdot (-2b) \cdot (-d)) + (b \cdot (-2b) \cdot 3c) + (b \cdot (-2b) \cdot (-d)) \\
&= 12a^2c - 4ad + 3abc - bd - 24abc + 8abd - 6b^2c + 2bd \\
&= (12a^2c - 24abc - 6b^2c) + (-4ad + 3abc + 8abd + 2bd) \\
&= 12ac(a - 2b) - 2bd(2a - 1c) \\
&= 12ac(4a + b) - 2bd(3c - d).
\end{align*}
\]
Therefore, the simplified expression is \(12ac(4a + b) - 2bd(3c - d)\).