Based on the relationship between each polygon and the number inside it, the value of ‘X’ is ________

The correct option is 720.

To find the value of ‘X’, we analyze the mathematical relationship between each polygon and the number inside it by counting the number of sides of each shape:
1. The first shape is a triangle, which has 3 sides. The number inside it is 6.
2. The second shape is a square, which has 4 sides. The number inside it is 24.
3. The third shape is a pentagon, which has 5 sides. The number inside it is 120.
4. The fourth shape is a hexagon, which has 6 sides. The number inside it is the unknown value ‘X’ (shown as 720 in the reference image).

By observing these numbers, we can see that the number inside each polygon is equal to the factorial of its number of sides ($n!$). Let us calculate the value for each shape:

For the triangle ($n=3$):
$$3!=3\times 2\times 1=6$$

For the square ($n=4$):
$$4!=4\times 3\times 2\times 1=24$$

For the pentagon ($n=5$):
$$5!=5\times 4\times 3\times 2\times 1=120$$

For the hexagon ($n=6$):
$$6!=6\times 5\times 4\times 3\times 2\times 1=720$$

Thus, the value of ‘X’ corresponding to the 6-sided hexagon is 720.