To find the perimeter of the regular hexagon, we can follow these steps:

1. In a regular hexagon, the line segment from the center $O$ to any vertex (in this case, the 18-unit segment) is the radius of the hexagon's circumscribed circle. This also represents the side length of the hexagon because all sides of a regular hexagon are equal to the distance from the center to any vertex.

2. Since we know each side of the hexagon is 18 units, and there are 6 sides in a hexagon, we can calculate the perimeter $P$ by multiplying the side length by 6:

   $P = 6 \times 18 = 108 \text{ units}$

Therefore, the perimeter of the hexagon is 108 units.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How would the perimeter change if the radius of the hexagon was doubled?
2. What is the area of this hexagon given the side length?
3. How does the perimeter of a hexagon compare to that of an equilateral triangle with the same side length?
4. What properties of a regular hexagon make each side equal to the radius from the center to a vertex?
5. How would you calculate the perimeter if the shape was an octagon with the same radius?

Tip: For regular polygons, each side length equals the distance from the center to any vertex when the polygon is inscribed in a circle.