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.
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When people are divided into groups of 6 or 9, then the LCM is 18
Next multiple of 18 in between 40 and 60 is 54.
Now the total number of people must be 54+4 = 58, as 4 people were sat in the car earlier.

If 5 people are sent in each car then 3 member are left who took taxi.

D is correct.
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My Approach:

So at first you feel question says the number of people can be >40 and <60 and it has to be divided in group of 5. So It can be 45,50, or any other number leaving the question ambiguous.
So let's try to find the number of people from information prior to it: If I subtract 4 from number the number is multiple of both 6 and 9. So if you think of it 6*9+4 itself results in 58 and is between 40 and 60.
Which means your number is 58.
So if 58 is divided by 5 the remainder is 3.
Hence D.
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