Hello, dhruviboy!

A pair has GCD 2 if both numbers are even.{ 2 3 4 5 6 7 8 9 }

In how many ways you can obtain 4 pairs with no pair having a GCD 2?

. . Hence, we must form pairs in which one is odd and one is even.

We have the four odd numbers: .

In how many ways can the even numbers be assigned?

The "2" can be paired with any of the 4 odd numbers.

Then the "4" can be paired with any of the remaining 3 odd numbers.

Then the "6" can be paired with either of the remaining 2 odd numbers.

And the "8" is paired with the 1 remaining odd number.

Therefore, there are: . possible pairings.