• 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.

My guess is 76.

If it is a multiple of 3, then it must be a multiple of 4, but not 6. This is impossible, since the LCM of 3 and 4 is 12, and 12 is a multiple of 6.

Therefore, it is not a multiple of 3. Since this is so, it cannot be a multiple of 6 either, since 6 is a multiple of 3.

The number must be either 70, 71, 73, 74, 76, 77 or 79. Since it is out of the non-multiple of 4 range, it must be 76, the only multiple of 4.

Regards,
wcaexqdz