To graph the inequality $x \leq 2$ on a number line, follow these steps:

1. Draw the Number Line: Begin by sketching a horizontal line to represent the number line.

2. Mark Important Points: Identify and mark several key points along this line, ensuring to include the number $2$.

3. Indicate the Inclusion of 2: Since the inequality is $x \leq 2$, it is essential to include the number $2$ in your solution set. To indicate this, place a filled (or solid) circle at the point corresponding to $2$ on the number line. The filled circle signifies that $2$ is part of the solution.

4. Shade the Appropriate Region: Next, to represent all numbers that are less than $2$, which lie to the left of $2$ on the number line, you will need to shade that area. Draw an arrow or shade the region extending from the filled circle at $2$ towards the left side of the number line. This shading indicates that all numbers to the left of $2$, including negative numbers and fractions, are included in the solution set for $x \leq 2$.

5. Highlight the Importance of the Filled Circle: It is crucial to note that the filled circle at $2$ indicates that $2$ is included in the solution. If the inequality were $x < 2$ instead, you would use an open circle at $2$ to show that $2$ is not part of the solution.

By following these steps, you can accurately and clearly represent the inequality $x \leq 2$ on a number line.