To find the outcomes of rolling an even number that is also divisible by 3 on a 6-sided number cube (which has the numbers 1 through 6), we identify the even numbers first: {2, 4, 6}.
Next, we check which of these even numbers are divisible by 3. The only even number in this set that is divisible by 3 is 6.
Thus, the outcome for rolling an even number divisible by 3 is:
{6}
So the correct response is:
{6}