Concept:
In a standard carrom game, the two players sit directly opposite each other.
If one player is facing a particular direction, the player sitting opposite must face the exactly opposite direction.
Step 1: Identify Sangeetha's facing direction.
Sangeetha is facing:
\[
\text{North-West}
\]
Step 2: Determine the opposite direction.
Opposite direction pairs are:
\[
\text{North} \leftrightarrow \text{South}
\]
\[
\text{East} \leftrightarrow \text{West}
\]
Therefore,
\[
\text{North-West}
\]
is opposite to
\[
\text{South-East}
\]
Step 3: Apply the standard carrom seating rule.
Since Sudha is sitting directly opposite Sangeetha, Sudha must face:
\[
\text{South-East}
\]
Step 4: Write the final answer.
\[
\boxed{\text{South-East}}
\]
Hence, option (D) is correct.