There are $4$ separate large boxes, and inside each large box there are $3$ separate small boxes, and inside each of these small boxes there are $2$ separate smaller boxes. How many boxes, counting all sizes, are there altogether?
$$
\begin{array}{|c|c|c|c|c|}
\hline
\textbf{Type of Box} & \textbf{Large} & \textbf{Small} & \textbf{Smaller} & \textbf{Total} \\
\hline
\textbf{Number} & 4 & 12 & 24 & 40 \\
\hline
\end{array}
$$ Therefore the answer is $\boxed{40}.$