If "fancy" numbers are defined as those whose digits sum to 9 then we have to ensure that if the first digit is 6, the remaining three digits must sum to 3. Since we are starting with 6 and 8, which already sum to 14, greater than 9, then the first digit is 7. The remaining digits must sum to 2. So the only possible 3-digit numbers are: 002, 011, 020, 101, 110, 200.
The fancy numbers are: 7002, 7011, 7020, 7101, 7110, 7200.
If fancy numbers are defined as those whose digits sum to 9 or a multiple of 9 (whose digits always sum to 9) then we are looking for all numbers between 6800 and 7800 divisible by 9.
6804, 6813, 6822, ..., 7002, 7011, 7020, 7029, 7038, ..., 7101, 7110, 7119, 7128, ..., 7200, 7209, 7218, ..., 7767, 7776, 7785, 7794. There would be 111 fancy numbers.