Ms. X came out of the building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing____

The correct answer is South.

Let's break down the step-by-step reasoning to determine the direction the building is facing, as illustrated in the provided diagram:
1. Determine the Position of the Sun and the Shadow:
According to the question and the illustration, it is morning. In the morning, the sun rises in the East. As shown in the diagram, the sun is positioned on the eastern side, and an arrow points from "(morning)" to "(East)".
Since light travels in straight lines, the shadow of any object will be cast in the opposite direction of the light source. Therefore, because the sun is in the East, Ms. X's shadow must fall towards the West.

2. Determine Ms. X's Orientation:
The problem states that Ms. X finds her shadow falling to her right side.
Since we already established that the shadow must fall towards the West, this means her right side is facing West (labeled as "Right (west)" in the diagram).
Consequently, her left side must be facing East (labeled as "Left (east)" in the diagram), looking towards the sun.
If a person's right side is facing West and their left side is facing East, they must be facing South.

3. Determine the Direction the Building is Facing:
Ms. X came out of the building through its front door and has the building to her back. This means she is walking in the direction that the front of the building faces.
Since she is facing and walking towards the South (indicated by the downward arrow pointing towards "South" from the stick figure in the diagram), the building's front door faces South.