$$
\begin{array}{l}
\left(a_{1}+a_{2}+a_{3}\right)\left(b_{1}+b_{2}+b_{3}+b_{4}\right) \\
\cdot\left(c_{1}+c_{2}+c_{3}+c_{4}+c_{5}+c_{6}\right)\left(d_{1}+d_{2}\right)
\end{array}
$$

How many different terms are there in the expanded form of the polynomial product?
In the expansion, each term has the form $a_{i} b_{j} c_{k} d_{l}$, where $i \in A_{1}=\{1,2,3\}, j \in A_{2}=\{1,2,3,4\}, k \in A_{3}=\{1,2,3,4,5,6\}, l \in A_{4}=\{1,2\}$. Therefore, this is a 4-fold selection problem. By the multiplication principle, the expansion contains
$$
\left|A_{1}\right| \cdot\left|A_{2}\right| \cdot\left|A_{3}\right| \cdot\left|A_{4}\right|=3 \times 4 \times 6 \times 2=144
$$

different terms.