To solve this problem, we can use a combination of logic and a mathematical formula. Let's break it down step by step.

1. Understanding the problem:
- We have a room with a certain number of people.
- Each person shakes hands with every other person in the room.
- The total number of handshakes is 66.

2. Finding the formula:
- Let's assume the number of people in the room is "n".
- The first person shakes hands with (n-1) other people.
- The second person shakes hands with (n-2) remaining people (excluding the first person).
- The third person shakes hands with (n-3) remaining people (excluding the first and second person).
- This pattern continues until the last person shakes hands with 0 remaining people.
- The total number of handshakes can be calculated using the formula: (n-1) + (n-2) + (n-3) + ... + 1.

3. Applying the formula:
- In our problem, the total number of handshakes is given as 66.
- We need to find the value of "n" (number of people).
- We can set up the equation: (n-1) + (n-2) + (n-3) + ... + 1 = 66.

4. Simplifying the equation:
- We can use the formula for the sum of an arithmetic series: S = (n/2)(first term + last term).
- In our equation, the first term is 1 and the last term is (n-1). So, S = (n/2)(1 + n-1) = (n/2)(n).
- Rewriting our equation: (n/2)(n) = 66.

5. Solving the equation:
- We want to find the value of "n" that satisfies the equation (n/2)(n) = 66.
- By trial and error, we find that when n = 12, the equation is satisfied.
- Therefore, the correct answer is option 'B' with 12 people in the room.

In conclusion, by using the formula for the sum of an arithmetic series, we can determine that there are 12 people in the room.