Explanation:

- Three circles each with a radius of 63 cm are arranged such that they touch each other.

- The problem involves equilateral triangle geometry formed by the centers of the circles.

- The side of the equilateral triangle formed is 126 cm (twice the radius).

- The formula for the area of the equilateral triangle is \((\sqrt{3}/4) \times \text{side}^2\).

- The sector area of each circle involved in the region calculation needs to be subtracted.

- Calculating this gives potential results matching the options.

- Option 1: \(7938\sqrt{3} - 4158\) does not properly match calculations.

- Option 2: \(3969\sqrt{3} - 4158\) also doesn’t align.

- Option 3: \(7938\sqrt{3} - 6237\) overshoots calculated areas.

- Option 4: \(3969\sqrt{3} - 6237\) correctly represents the enclosed area calculation after proper sector and triangle adjustments.