Step 1: Look at how each number grows from the one before it:
Instead of jumping straight to a formula, we check what number we multiply by to go from one shape's number to the next shape's number.
Step 2: Find the first multiplier.
Going from the triangle's 6 to the rectangle's 24 gives $24 / 6 = 4$. Notice 4 is the number of sides of the rectangle itself.
Step 3: Find the second multiplier.
Going from the rectangle's 24 to the pentagon's 120 gives $120 / 24 = 5$. Again 5 is the number of sides of the pentagon itself.
Step 4: Spot the pattern and use it.
Each new number is the old number multiplied by the side count of the new shape. The hexagon has 6 sides, so we multiply the pentagon's 120 by 6.
\[ X = 120 \times 6 = 720 \]
Step 5: Check option (A) 720.
This matches the value from Step 4, so this option is correct.
Step 6: Check option (B) 596.
596 is not 6 times 120 and breaks the multiplier pattern found in Steps 2 and 3, so this option is wrong.
Step 7: Check option (C) 24.
24 belongs to the earlier rectangle shape and does not come from multiplying 120 by 6, so this option is wrong.
Step 8: Check option (D) 240.
240 is only 120 multiplied by 2, not by 6, so it does not follow the pattern and is wrong.
Final Answer:
Multiplying step by step through the side counts also gives 720.
\[ \boxed{X = 720} \]
