<human>: [Instruction]
<bot>:

"""<human>: A positive integer $X$ is 2 more than a multiple of 3. Its units digit is the same as the units digit of a number that is 4 more than a multiple of 5. What is the smallest possible value of $X$?
<bot>:"""

I need to find a positive integer $X$ that satisfies two conditions: $X$ is 2 more than a multiple of 3, and its units digit is the same as the units digit of a number that is 4 more than a multiple of 5.
I can start by listing some multiples of 3 and their units digits: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.
I can also list some multiples of 5 and their units digits: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.
I notice that the units digit of a multiple of 3 is always 3, and the units digit of a multiple of 5 is always 5.
This means that the units digit of $X$ must be 3, and the units digit of $X$ must be 5.
The only multiple of 3 that is 2 more than a multiple of 3 is 6, and the only multiple of 5 that is 4 more than a multiple of 5 is 19.
Therefore, the smallest possible value of $X$ is 6.

# Answer

6