Correct Option (C)

The area of the rectangular piece of tin is determined by multiplying its length and width. Given the length as 12 cm and the width as 8 cm, the area of the tin is 12 cm × 8 cm = 96 cm².

When this rectangular tin is utilized to construct a closed cube, the total surface area of the cube must correspond to the area of the tin sheet. The formula for the total surface area of a closed cube with side 'a' is 6a².

Equating the area of the tin sheet to the surface area of the cube:

$6 a^{2} = 96$

To find the side 'a', we solve the equation:

$a^{2} = \frac{96}{6}$

$a^{2} = 16$

$a = \sqrt{16}$

$a = 4 cm$

Therefore, the side of the constructed cube is 4 cm.

Incorrect Options:

The side of the cube must yield a total surface area of 96 cm² to be consistent with the area of the tin sheet.

If the side of the cube were 2 cm (Option A), its total surface area would be $6 \times (2 cm)^{2} = 6 \times 4 {cm}^{2} = 24 {cm}^{2}$ , which does not match the available tin area of 96 cm².
If the side of the cube were 3 cm (Option B), its total surface area would be $6 \times (3 cm)^{2} = 6 \times 9 {cm}^{2} = 54 {cm}^{2}$ , which is not equal to 96 cm².
If the side of the cube were 6 cm (Option D), its total surface area would be $6 \times (6 cm)^{2} = 6 \times 36 {cm}^{2} = 216 {cm}^{2}$ , which significantly exceeds the available tin area of 96 cm².