12. (17 points) A rectangular wooden board, if 4 decimeters are cut off from both the longer and shorter sides, the area is reduced by 168 square decimeters. Please ask: What is the original perimeter of the rectangle in decimeters?


【Analysis】As shown in the figure:
Assuming the length and width are each reduced by 4 decimeters, the remaining length is $b$ decimeters, and the remaining width is $a$ decimeters, then the area of the removed part is: $4 b+4 a+4 \times 4=168$, solving for $a+b=(168-16) \div 4=38$, the original rectangle's perimeter is: $(b+4+a+4) \div 2$, substitute the value of $(a+b)$ to calculate accordingly.
【Solution】Solution: As shown in the figure:
Let the length and width be each reduced by 4 decimeters, the remaining length is $b$ decimeters, and the remaining width is $a$ decimeters,
$$
\begin{aligned}
4 b+4 a+4 \times 4 & =168 \\
4(a+b) & =168-16 \\
4(a+b) & =152, \\
4(a+b) \div 4 & =152 \div 4 \\
a+b & =38,
\end{aligned}
$$

The original rectangle's perimeter is:
$$
\begin{aligned}
& (b+4+a+4) \times 2 \\
= & (38+8) \times 2 \\
= & 46 \times 2 \\
= & 92 \text { (decimeters). }
\end{aligned}
$$

Answer: The original rectangle's perimeter is 92 decimeters.