12. (5 points) Person A and Person B start from points $A$ and $B$ respectively at the same time, heading towards each other, and they can meet after 4 hours; if both increase their speed by 3 kilometers per hour, they can meet after 3 hours and 30 minutes. The distance between $A$ and $B$ is $\qquad$ kilometers.
【Analysis】To find the distance between two places, we need to determine the corresponding speed. According to the formula speed $=$ distance difference $\div$ time difference, we can find the speed, and then multiply it by the corresponding time to solve the problem.

【Solution】Solution: According to the later travel time of 3.5 hours, in 3.5 hours, the additional speed per hour is $3+3$ $=6$ km/h.

The original speed is: $6 \times 3.5 \div(4-3.5)=42$ km/h.
The distance between $A$ and $B$ is: $42 \times 4=168$ (km).
Therefore, the answer is: 168