Explanation:
first of all, distance and displacement are simply geographic measurements. there is no time or time period involved. your description under 1. is 100% correct.
but then, all your calculations of 2. to 4. are suddenly all based on time and time differences. that is wrong, as it has nothing to do with the questions about displacements.
when somebody simply walks around the block one time ending up at the same location as he/she started, then the displacement is 0 meters (the end position is 0 meters distant from the starting position). but the distance walked is the perimeter of the rectangle or square of the block. that is the difference between the 2 terms. there is no time involved for that. asking about the speed vs. the velocity that would be a completely different matter.
2.
from 0 to 4 second the person simply walks to the car. and the displacement at the end of the 4 seconds is
6 meters.
3.
from 4 to 6 seconds the person stays at the car (clearly looking for the bag and grabbing it). there is no change in the position or distance to the starting point.
the displacement is therefore 0 meters.
4.
from 6 seconds to 8 seconds the person walks back to the original starting point (distance is 0).
so, the displacement is 6 meters.
but you see, the displacement between 0 and 8 seconds is 0 meters, as the person ends up at the same point he/she started at.
5.
the distance the person traveled was 6 meters between 0 and 4 seconds, 0 meters between 4 and 6 seconds, and 6 meters between 6 and 8 seconds.
distance = 6 + 0 + 6 = 12 meters.
6.
speed and velocity are expressed as ratio
distance traveled / time passed
so,
6 meters / 4 seconds = 6/4 m/s = 3/2 m/s
in this case speed = velocity, because the person moved only in one direction.
7.
there is a typo in the question. the person is walking back to his/her home (not hour).
the velocity is now
6 meters / 2 seconds = 6/2 m/s = 3 m/s
again, speed = velocity, because the person walked only in one direction.
8.
6. and 7. tell us that the speed of walking back was faster (twice as fast) than walking towards the car.
we know that because 3 (m/s) is larger than 3/2 (m/s). so, the speed is higher.
9.
the position at 2 seconds is at 3 meters. that means 3 meters away from home and 3 meters still away from the car (right in the middle).
10.
the person moved 6 + 0 + 6 = 12 meters in 8 seconds.
so, the average speed was
12 meters / 8 seconds = 12/8 m/s = 3/2 m/s.
that is possible, because of the 2 seconds the person was stationary in between (0 m/s speed).