We could use a calculator to divide each of the four given numbers by 3 to see which calculations give an integer answer. Alternatively, we could use the fact that a positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. The sums of the digits of $222, 2222, 22222$, and $222222$ are $6, 8, 10$, and 12, respectively. Two of these sums are divisible by 3 (namely, 6 and 12) so two of the four integers (namely, 222 and 222222) are divisible by 3.