To find the perimeter of a square, you can use the formula:
\[ \text{Perimeter} = 4 \times \text{side length} \]
In this case, the side length of the square is 6 inches.
Calculating the perimeter:
\[ \text{Perimeter} = 4 \times 6 \text{ inches} = 24 \text{ inches} \]
Therefore, the perimeter of the piece of paper is 24 inches.