8. (10 points) There is a rectangle. If its length and width are both increased by 6 cm, then the area increases by 114 square cm. The perimeter of this rectangle is $\qquad$ cm.
【Analysis】As shown in the figure: Since the original rectangle's length $\times 6+$ original rectangle's width $\times 6+6 \times 6=114$ square centimeters, according to the distributive law of multiplication, we can find the original rectangle's length + width, and thus find the original rectangle's perimeter.

【Solution】Solution: $(114-6 \times 6) \div 6 \times 2$,
$$
\begin{array}{l}
=(114-36) \div 6 \times 2, \\
=78 \div 6 \times 2, \\
=13 \times 2, \\
=26 \text { (cm), }
\end{array}
$$

Answer: The perimeter of this rectangle is 26 cm.
Therefore, the answer is: 26.