A certain number of cars were arranged by a hotel to escort its custom

Because they say there are either 6 people in each car, or 9 in each car after removing 4 people, the remaining number must be divisible by both 6 and 9, so by the LCM of 6 and 9, which is 18. Since the total is between 40 and 60, we must have 54 people after removing four of them, so 58 people in total, and the answer to the question is 3.

It's possible they intend a different meaning here (because they're not even using articles correctly, I find it difficult to be confident I'm interpreting the wording properly). If instead they mean that some of the remaining people go in 6-person cars, and some in 9-person cars, then the total (after removing four) can be any multiple of 3. So we could have 51 people, by, say, putting 6 people in seven cars, and 9 people in one car. Then we have 55 people in total (adding back the four extra people), and the answer to the question would be 0. But as the question is written, the answer is 3.