Let the missing numbers be positive integers a, b, c, d in order from top to bottom. Assume that in each row and column the numbers are in ascending order.
3 25 a 65
b 30 47 69
16 c 58 72
19 37 59 d
From the assumption that the numbers are ordered, 25<a<47, 3<b<16, 30<c<37, d>72.
Now we need to find some pattern. We can eliminate a common sum of the numbers in each row or column, particularly because the second rows would imply that b=c which contradicts our assumptions about order (the sum of the known numbers is 146 for both rows).
The tentative solution below is based on: b-3=30-25, b=8; 47-a=69-65, a=43; 37-c=19-16, c=34; d-72=59-58, d=73. The link between rows 2, 3 and 4 is 72-69=19-16=3.
3 25 43 65
8 30 47 69
16 34 58 72
19 37 59 73