Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are $6$ empty chairs, how many people are in the room?

$\textbf{(A)}\ 12\qquad
\textbf{(B)}\ 18\qquad
\textbf{(C)}\ 24\qquad
\textbf{(D)}\ 27\qquad
\textbf{(E)}\ 36$
1. Let \( C \) be the total number of chairs in the room. According to the problem, there are 6 empty chairs, which represent \(\frac{1}{4}\) of the total chairs. Therefore, we can write:
   \[
   \frac{1}{4}C = 6
   \]
   Solving for \( C \), we multiply both sides by 4:
   \[
   C = 6 \times 4 = 24
   \]
   So, there are 24 chairs in total.

2. Next, we need to find the number of chairs that are occupied. Since \(\frac{1}{4}\) of the chairs are empty, \(\frac{3}{4}\) of the chairs are occupied. Thus, the number of occupied chairs is:
   \[
   \frac{3}{4} \times 24 = 18
   \]
   Therefore, 18 chairs are occupied.

3. According to the problem, \(\frac{2}{3}\) of the people are seated in \(\frac{3}{4}\) of the chairs. Let \( P \) be the total number of people in the room. We know that \(\frac{2}{3}\) of the people are seated, and this number is equal to the number of occupied chairs:
   \[
   \frac{2}{3}P = 18
   \]
   Solving for \( P \), we multiply both sides by \(\frac{3}{2}\):
   \[
   P = 18 \times \frac{3}{2} = 27
   \]
   Therefore, the total number of people in the room is 27.

The final answer is \(\boxed{27}\)