The number of Turkmen's for whom exactly four of the six music forms are in vogue is at least
We need to find the minimum of exactly 4 out of 6. If we consider each of the sets to be represented as straight lines, what the question asks is to minimize the region of 4 lines of overlap. This means that we can make more than 4 lines or less than 4 lines overlap to the maximum possible.
If you notice the representation above, there is no region where 4 lines are overlapping, hence, the minimum region of 4 lines of overlap is 0. Option (e)