Question 565182
Positive whole numbers less than 100 means at most two digits, but
Two digit numbers where the ten’s digit is greater than the one’s digit implies exactly 2 digits.
Four more than each number is a multiple of 6 means even numbers, because an odd number plus 4 would still be odd and could not be a multiple of 6. So the ones number could be 0, 2, 4, 6, or 8.
The last two conditions
3. The sum of the digits of each number is a multiple of 4. 
4. Two digit numbers where the ten’s digit is greater than the one’s digit
limit choices even further.
If the ten’s digit is greater than the ones digit, the ones digit cannot be 8. (The tens digit would have to be 9, and then the sum would be odd.
The ones digit has to be 0, 2, 4, or 6.
If the ones digit is 6, adding a greater tens digit (could only be 7, 8, or 9) would make the sum of digits 13, 14, or 15, and it would not be a multiple of 4.
If the ones digit is 4, we can make a multiple of 4 by adding 8 as the tens digit (5, 6, 7, and 9 do not work). The number would be 84, which is a multiple of 6, so that four more than 84 (88) would NOT be a multiple of 6.
Maybe the ones digit could be 2. Adding 6 as the tens digit would make the sum a multiple of 4 (2+6=8). Other numbers (3, 4, 5, 7, 8, or 9) do not work as tens digit. The number would be 62, and adding 4 we would get 66, which is a multiple of 6.
Our first answer is {{{highlight(62)}}}.
Or maybe the ones digit is zero. Then the tens digit could be 4 or 8, and the digits would add up to a multiple of 4. The numbers would be 40 or 80. Adding 4 to each we get 44 (not a multiple of 6) and 84 (6 times 14).
So our second and last answer is {{{highlight(80)}}}.