Explanation:

Let,
Sum of Even numbers be: \((a - 2) + a + (a + 2)\)
Sum of Odd numbers be: \((b - 4) +(b - 2) + (b + 2) + (b + 4)\)

Given, \((b - 4) +(b - 2) + (b + 2) + (b + 4) = (a - 2) + a + (a + 2)\)
\(4b = 3a\)
\(a = \frac{4b}{3}\)

This means, \(b\) has to be a multiple of 3 which will make \(a\) as the multiple of 4

Also, \(101 < a < 200\)
i.e. \(102 ≤ \frac{4b}{3} ≤ 198\)

\(102(\frac{3}{4}) ≤ b ≤ 198(\frac{3}{4})\)

\(76.5 ≤ b ≤ 148.5\)

Since, \(b\) is odd, it can have \(\frac{(147 - 77)}{2} + 1 = 36\) values in total

But, it has to be a multiple of 3 as well, so we can have \(\frac{36}{3} = 12\) values for \(b\)
Therefore, \(a\) can take 12 values too.

Col. A: 12
Col. B: 12

Hence, Option C