Q24

Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows

$$P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\}$$

The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.