6. (10 points) As shown in the figure, a rectangular piece of paper is 20 cm long and 16 cm wide. If a small rectangle 8 cm long and 4 cm wide is cut from this paper, and at least one side of the small rectangle is on the edge of the original rectangle, then the maximum perimeter of the remaining paper is ( ) cm.
A. 72
B. 80
C. 88
D. 96
【Analysis】As shown in Figure (1): A rectangle 8 cm long and 4 cm wide is cut from one corner, and the perimeter of the remaining paper piece is equal to the original rectangle. According to the perimeter formula of a rectangle: $c=(a+b) \times 2$, substitute the data into the formula to solve. As shown in Figure (2), if a rectangle 8 cm long is cut along the original edge with a width of 4 cm, then the perimeter of the remaining paper piece will increase by $8+8=16$ cm. Solve accordingly.

【Solution】Solution: (1) $(20+16) \times 2$,
$$
\begin{array}{l}
=36 \times 2, \\
=72 \text { (cm), }
\end{array}
$$
(2) $(20+16) \times 2+8 \times 2$,
$$
\begin{aligned}
= & 36 \times 2+16, \\
= & 72+16, \\
= & 88 \text { (cm), }
\end{aligned}
$$

Answer: The maximum perimeter of the remaining paper piece is 88 cm.
Therefore, the correct choice is: $C$.