25) B
Since all eight digits have to different, one clock must show 19 in the hours place and the second clock must show 20 in the hours place.
When the correct time is 20:00, the first clock must show 19:44 and the second clock must show 20:25
The successive minutes must be within the range of 19:44 and 19:59 for the first clock and within the range of 20:25 and 20:41 for the second clock.
Since all eight digits have to different, the clocks cannot show 1, 9, 2 or 0 in the minutes as these numbers are in the hours of the first and the second clock. Since the second clock cannot show 2 in the minutes, the second clock must show minutes which are after 20:31.

When it is 20:31 in the second clock it is 19:50 in the first clock. This cannot be correct as there is 0 in both clocks.
20:34 = 19:53. This is wrong as 3 in both clocks
20:35 = 19:54. This is wrong as 5 in both clocks
20:36 = 19:55. This is wrong as 5 is repeated in clock 1
20:37 = 19:56. This could be correct
20:38 = 19:57. This could be correct
20:39 = 19:58. This is wrong as 9 repeated in both clocks
20:40 = 19:59. This is wrong as 0 repeated in clock 2
20:41 = 20:00. This is wrong as 2 and 0 repeated in both clocks

The consecutive minutes are 20:37-19:56 and 20:38-19:57.
The options given to us are 3, 4, 5, 6, 7 and 8. Out of these options, 3, 5, 6, 7 and 8 appear on the clocks during the consecutive minutes. This means that the answer is 4