Atharv starts from Point A and drives 12 km towards west. He then takes a right turn, drives 3 km, turns right and drives 16 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degree turns only unless specified.)

The correct answer is 6 km to the north.

Let us trace Atharv's movement step-by-step starting from Point A, using a standard Cartesian coordinate system where Point A is at the origin $(0,0)$.
Let East be the positive x-axis, West be the negative x-axis, North be the positive y-axis, and South be the negative y-axis.

Step 1: Start at Point A
Starting position: $(0,0)$

Step 2: Drive 12 km towards West
Moving west decreases the x-coordinate by 12.
Position after 1st leg: $(0-12,0)=(-12,0)$

Step 3: Turn right and drive 3 km
Facing West, a right turn means facing North. Moving north increases the y-coordinate by 3.
Position after 2nd leg: $(-12,0+3)=(-12,3)$

Step 4: Turn right and drive 16 km
Facing North, a right turn means facing East. Moving east increases the x-coordinate by 16.
Position after 3rd leg: $(-12+16,3)=(4,3)$

Step 5: Turn right and drive 9 km
Facing East, a right turn means facing South. Moving south decreases the y-coordinate by 9.
Position after 4th leg: $(4,3-9)=(4,-6)$

Step 6: Take a final right turn, drive 4 km and stop at Point P
Facing South, a right turn means facing West. Moving west decreases the x-coordinate by 4.
Final position at Point P: $(4-4,-6)=(0,-6)$

Determining direction and shortest distance to reach Point A:
Point A is located at $(0,0)$ and Point P is located at $(0,-6)$.

To reach Point A $(0,0)$ from Point P $(0,-6)$:
Distance = $0-(-6)=6\text{ km}$
Direction = Towards positive y-axis, which is North.

Therefore, Atharv needs to drive 6 km to the north to reach Point A again.