Help on problem - counting and/or number theory

Sorry, can't read your "condition"!.

I revised it.

If I understand the question...

LCM [ 6, 8 ]  =  24

The multiples of 24 between 100 and 200 are  :

n = 120, 144, 168, 192    

So...n will have the same remainder  when divided by 6 or 8

All of the following numbers will give the same remainder for both, 6 and 8 ranging from 0 to 5:
n =100, 101, 120, 121, 122, 123, 124, 125, 144, 145,146, 147, 148, 149, 168, 169,170, 171, 172, 173, 192, 193, 194, 195, 196, 197. 

Thank you!