Explanation:

To solve this problem, you need to use geometry and algebra:

- Consider two circles intersecting at points P and Q.

- The radii of the circles are given as 10 cm and 8 cm.

- The distance PQ, which is a common chord of the circles, measures 12 cm.

- To find x, the distance between the centers, you can use the formula involving the power of the point:

$$

x = \sqrt{d_1^2 - (PQ/2)^2} + \sqrt{d_2^2 - (PQ/2)^2}

$$

$$

x = \sqrt{10^2 - 6^2} + \sqrt{8^2 - 6^2}

$$

$$

x = \sqrt{100 - 36} + \sqrt{64 - 36}

$$

$$

x = \sqrt{64} + \sqrt{28}

$$

$$

x = 8 + \sqrt{28}

$$

- Simplify $\sqrt{28}$ to approximately 5.3, resulting in:

$$

x = 8 + 5.3 = 13.3

$$

- Option 2: 13.3 is the correct answer.