if i walk 4 miles turn and walk 1 mile turn and walk 3 miles and end up back where i started at what is my displacement
Your displacement is the straight line distance from your starting point to your ending point.
If you walk 4 miles, turn, and walk 1 mile in the opposite direction, you would have walked a total of 3 miles in one direction.
Then, if you turn again and walk 3 miles in the opposite direction, you would end up back at your starting point.
Therefore, your displacement is 0 miles because you ended up at the same spot where you started.