If a number is divisible by both 2 and 3, then it will be divisible by 6 also.
And a number will be divisible by 8 only if the last three digits are divisible by 8.
For 9648, it is divisible by both 2 (since it is an even number) and 3 (since 9+6+4+8 = 27 which is divisible by 3 ).
The last 3 digits, i.e. 648 is also divisible by 8
So, 9648 is divisible by both 6 and 8.