Solution: 38
Work: The even numbers that are 2-digit are 10, 12, 14, ..., 98.
The even numbers that are multiples of 3 and even are multiples of 6: 12, 18, 24, ..., 96.
There are 5, 6, 7, ..., 49=44 2-digit even numbers and
2, 3, 4, ..., 16= 15 multiples of 6 that are 2 digit.
44-6=38 2-digit numbers that are multiples of 2, but not 3.
Solution: 30
Work: The even numbers that are 2-digit are 10, 12, 14, ..., 98.
The even numbers that are multiples of 3 and even are multiples of 6: 12, 18, 24, ..., 96.
There are 5, 6, 7, ..., 49=45 2-digit even numbers and
2, 3, 4, ..., 16= 15 multiples of 6 that are 2 digit.
45-15=30 2-digit numbers that are multiples of 2, but not 3.
I think the Guest that answered got everything correct except for what I corrected.
