Explanation:

- We have a quadrilateral ABCD with known side lengths: AB = 6 cm, BC = 18 cm, CD = 6 cm, and DA = 10 cm.

- The diagonal BD splits the quadrilateral into two triangles: ABD and BCD.

- In triangle ABD, the sides are AB = 6 cm, DA = 10 cm, and BD = x. The triangle inequality rule tells us: 6 + 10 > x, 6 + x > 10, and 10 + x > 6. From these, we find x < 16.

- In triangle BCD, the sides are BC = 18 cm, CD = 6 cm, and BD = x. The triangle inequality rule tells us: 18 + 6 > x, 18 + x > 6, and 6 + x > 18. From these, we find x > 12.

- Combining both results, 12 < x < 16.

Option 2: 12 < x < 16 is correct.