There are 8 cutting machines and each machine can cut 4 cases every 15 seconds, or 16 cases per minute (4 cases/15 seconds x 60 seconds/minute = 16 cases/minute). Therefore, all 8 machines can cut a total of 8 x 16 = 128 cases per minute.
If 25% of the machines are removed for maintenance, then 2 machines (25% of 8) will be taken out of service. This leaves 6 machines to continue cutting phone cases.
The 6 remaining machines can cut 6 x 16 = 96 cases per minute (since each machine still cuts 16 cases per minute). Therefore, the 6 remaining machines cut 128 - 96 = 32 fewer cases per minute than all 8 machines together.
So the answer is that the remaining machines cut 32 fewer cases per minute when compared to the number of cases per minute all 8 machines cut.