If the total distance between the two towns is 18km and you have already covered 14km by car, then you have 18km - 14km = <<18-14=4>>4km left to cover on foot.
Since 1km is equal to 1000m, then 4km is equal to 4 * 1000m = <<4*1000=4000>>4000m.
When someone offers you a lift 2km from the next town, then you only have to walk the remaining 4km - 2km = <<4-2=2>>2km.
2km is equal to 2 * 1000m = <<2*1000=2000>>2000m.
Therefore, you walked a total of 4000m - 2000m = <<4000-2000=2000>>2000m. Answer: \boxed{2000}.
The distance between two towns is 18km. If you travel by car and cover 14km of the distance between the two towns before your car breaks down, how many meters did you walk if someone offered you a lift 2km from the next town?
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