Given four numbers are in AP

Let the four numbers are a - 3d, a - d, a + d and a + 3d

Now, (a - 3d) + (a - d) + (a + d) + (a + 3d) = 40

=> 4a = 40

=> a = 40/4

=> a = 10

Now, product of extremes = (a - 3d)*(a + 3d) = (10 - 3d)*(10 + 3d) = 100 - 9d²

Again, product of means = (a - d)*(a + d) = (10 - d)*(10 + d) = 100 - d²

Given, Product of extremes : Product of means = 2 : 3

=> (100 - 9d² )/(100 - d² ) = 2/3

=> 3(100 - 9d² ) = 2(100 - d² )

=> 300 - 27d² = 200 - 2d²

=> 300 - 200 = 27d² - 2d²

=> 100 = 25d²

=> d² = 100/25

=> d² = 4

=> d = ± 2

Now, the numbers are: a - 3d, a - d, a + d and a + 3d

                             = 10 - 3*2, 10 - 2, 10 + 2 and 10 + 3*2

                             = 10 - 6, 10 - 2, 10 + 2 and 10 + 6

                             = 4, 8, 12, 16