Simply substitute the value of 'n' that are given in the options and see whose sum is equal to 72
Ex: Take n = 9,S9 = 9/2 [ 2(24) + (9-1)(-4)] = 9/2 [48 - 32] = 9/2*16 = 72
Similarly, take n = 4,S4 = 4/2 [2(24) + (4-1)(-4)] = 2[48 - 12 ] = 2*36 = 72

Problem Analysis:
We are given a series: 24, 20, 16, ...
We need to find out how many terms of this series are required so that their sum is 72.

Solution:
To find the sum of the series, we need to identify the pattern and the formula to calculate the sum.

Pattern:
If we observe the series carefully, we can see that each term is obtained by subtracting 4 from the previous term. So, the series can be written as:
24, 20, 16, 12, 8, ...

Formula:
The nth term of the series can be calculated using the formula:
nth term = first term + (n-1) * common difference

In this series, the first term (a) is 24 and the common difference (d) is -4.

So, the nth term can be calculated as:
nth term = 24 + (n-1) * (-4)
nth term = 24 - 4n + 4
nth term = 28 - 4n

Calculating the Sum:
To find the number of terms required to get a sum of 72, we can use the formula for the sum of an arithmetic series:

sum = (n/2) * (first term + last term)

We know that the sum is 72 and the first term (a) is 24.
Let's find the last term (l) using the formula for the nth term:

l = 28 - 4n

Now, we can substitute the values of sum, first term, and last term in the sum formula and solve for n:

72 = (n/2) * (24 + (28 - 4n))
72 = (n/2) * (52 - 4n)
72 = (n/2) * (52 - 4n)

Simplifying the equation:

72 = 26n - 2n^2
2n^2 - 26n + 72 = 0
n^2 - 13n + 36 = 0
(n - 9)(n - 4) = 0

So, the possible values of n are 9 and 4.

Conclusion:
The number of terms required to get a sum of 72 in the series 24, 20, 16, ... is either 9 or 4. Therefore, the correct answer is option 'c' (9 or 4).