23) E

Let us first figure out what each digit means.

The first three digits meant the month of operation of the clinic.

The 4th and 5th digits mean which date of the month the sample is taken. In the example given, 04 in 12404360 means 4th of September.
So, 04 = 4th

The 6th and 7th digits mean the the number of sample taken in that month.
36 in 12404360 means 36th sample.

The last digit is a digit which makes the sum of the eight digits a multiple of 10.
The sum of the first seven numbers in 12404360 = 1+2+4+0+4+3+6 = 20. This figure is already a multiple of 10 and hence the last digit must be 0.
In 25431438, the sum of the first seven digits = 22
In order to make this a multiple of 10 (30), we need to add 8 to 22 in order to make 30.

Let us find out which month’s reference number are given in the options.

Since, 124 is September,

A – 254 must be July. July has 31st
B – 264 must be May. May has 31st
C – 274 must be March. March has 31st
D – 284 must be January. January has 31st
E – 294 must be November. November does not have 31st. Hence, this is wrong.