Answer
The sequence $a_n$ is not monotonic and bounded.
Work Step by Step
Our aim is to find out if the sequence $a_n$ is monotonic.
In order to this, we will consider $a_n=\dfrac{2^n 3^n}{n!}=\dfrac{6^n}{n!}$ for all $n \in N$
Also, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty}\dfrac{6^n}{n!}=0$
Thus, $a_n$ is bounded because the sequence converges to $0$
Now, $a_1= \dfrac{6^1}{1!}=6 \lt a_2=\dfrac{6^2}{2!}$ but $a_6= \dfrac{6^6}{6!}\gt a_7=\dfrac{6^7}{7!}$
Hence, the sequence $a_n$ is not monotonic and bounded.
