6. (3 points) Reduce one side of a square by $2 \mathrm{~cm}$ and increase the other side by $20 \%$, resulting in a rectangle with the same area as the original square. What is the side length of the square? $\qquad$ $\mathrm{cm}$.
【Solution】Solution: Let the original side length of the square be $x \mathrm{~cm}$, according to the problem, we have:
$$
\begin{aligned}
1.2 x(x-2)-x^{2} & =0, \\
1.2 x-2.4-x & =0, \\
1.2 x-x & =2.4, \\
0.2 x & =2.4, \\
x & =12 .
\end{aligned}
$$

Answer: The side length of the square is $12 \mathrm{~cm}$.
Therefore, the answer is: 12 .