If we draw our rectangle from the bottom left corner starting at the origin, the first point will be (0,0).
Now for the rectangle to have a perimeter of 16, all the sides must add up to 16.
This can be achieved with sides of 5,5,3,3.
To get the next coordinate, lets move 5 units along the x-axis. This will put us at (5,0).
now 3 units up from there will give us (5,3)
Then -5 units along the x-axis from that point will give us (0,3)
Therefor the points are (0,0) (5,0) (5,3) (0,3)