There are 4 even numbers and 4 odd numbers
if an even and odd number is paired then no pair of gcd 2
which is 4!=24 ways.
the order of odd numbers can be shuffled that many different ways in each case pairing the first odd number with 2, the second one with 4, and so on.
if even and odd are not paired then
two even numbers is paired
here the pair of even numbers in the set that have gcd not 2 is 4 and 8.
so pair of 4 and 8 taken.
choose two odd numbers to pair together in {4 \choose 2}=6 different ways and pair the remaining two odd numbers in 2 different ways with 2 and 6
which gives (2)(6)=12 different ways
so two methods give 24+12=36 ways.
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