the moon is the fifth available item when initially asked to have a number 5-15 picked.

now there are only 12 possible selections and you are asked to move back the same number of spaces as before...(this is were the whole, 2 odds equal and even number, and 2 evens equal an even number come into play)...behind the pictures im sure its numbered as to what the even and odds are.

5-10
6-12
7-14
8-16
9-18
10-20
11-22
12-24
13-26
14-28
15-30

but notice the 3 small initial items were removed, 0-2, flipping the numbers available to odds instead of evens (except for #12, due to the removal).

he then removes initially numbered items 6, 8, 10, 14, and
now having only 8 left to choose from, you are asked to move 4 in either direction. and numbers 4, 12, 13 are removed. (13 is removed because it was unable to be selected, the #4 spot had no chance of being initially picked, once the 3 items were removed, 14 and 13 took their spots of unable to being landed on)

the final one left was #5....

so to put it in its easiest form...15 (number you started with) then move your number, X, subtract 3, and go X in the opposite direction...always ending up with 12.

15 - x - 3 + x = 12 (x's cancel, basically 15-3)

so being at initially numbered position 12, and pulling out all of the other evens, and the one odd that was unable to be a possibility, the #5 position is the 4th selection, going in either direction.