• if it is not a multiple of 4, then it is between 60 and 69
• if it is a multiple of 3 it is between 50 and 59
• if it is not a multiple of 6 it is between 70 and 79.

If it is not a multiple of 4, then the numbers can be:
61, 63, 65, 66, 67, 69.
But all these numbers except 66 are not a multiple of 6, so should be in the range 70-79 ; &
66 is divisible by 3, so should be in the range 50-59
so.. none of these is the chosen number.

If it is a multiple of 3, then the numbers can be:
51, 54, 57.
But again none of these are a multiple of 4, so should be in the range 60-69.
so.. none of these is the chosen number either.

if it is not a multiple of 6, then the numbers can be:
70, 71, 73, 74, 75, 76, 77, 79.
Except 76...None of these numbers are a multiple of 4, so should be in the range 60-69.

So the chosen number is 76