An even number is an integer of the form n=2k , where k is an integer and in our case k>0.

The 4 positive numbers can be written as 2a, 2b, 2c and 2d where a,b,c and are positive integers thus the sum will be

2a +2b + 2c + 2d = 24

2 (a+b+c+d) = 24 divide both sides by 2

a+b+c+d = 12

Let write them down

1,1,1,9

1,1,2,8

1,1,3,7

1,1,6,6

1,1,5,5

1,2,2,7

1,2,3,6

1,2,4,5

1,3,3,5

1,3,4,4

2,2,2,6

2,2,3,5

2,2,4,4

2,3,3,4

3,3,3,3

there are 15 possible ways (up to commutativity).