Woah that's a lot of words! First recall that the distance between two coordinate points is:
d = square root of (x2 - x1)^2 + (y2-y1)^2
Now Let's break the journey down into parts.
1) SWING SET TO JUNGLE GYM
(-4,2) to (5,2)

2) GYM TO TIRE SWING
(5,2) to (5,-4)

3) TIRE SWING TO SLIDE
(5,-4) to (-4,-4)
Now you try the last two!
You can comment the answer and I can check it.
The total distance will be the sum of all the line sections, so we'll need to add up all the d's. And since 1 unit = 1 yard there's no unit conversion. :)