You haven't provided the graph, therefore, I cannot provide you with a specific solution for this question. However, I will tell you how to solve it and you can apply on the graph you have.
Now, we are given that: x-axis represents the distance in ft y-axis represents the time in minutes
To get the time that she has walked when she reaches the farthest point from her house, all you have to do is: 1- go to the greatest point on the x-axis. This point would be representing the farthest distance. 2- get the value of the y corresponding to the x-point you got in step one. This would be the time walked when she reaches the farthest point which is the value you are looking for.
Since a side is only 6 inches long and the total perimeter is 36; take 36/6 and you get 6. The only figure with six sides is a hexagon, thus your answer is hexagon.