To solve this problem, we first need to convert each of the base-3 numbers to base-10, perform the arithmetic operation, and then convert the result back to base-3.

Let's start by converting each base-3 number to base-10:

- (212)\(_3\) = 2*(3^2) + 1*(3^1) + 2*(3^0) = 18 + 3 + 2 = 23
- (121)\(_3\) = 1*(3^2) + 2*(3^1) + 1*(3^0) = 9 + 6 + 1 = 16
- (222)\(_3\) = 2*(3^2) + 2*(3^1) + 2*(3^0) = 18 + 6 + 2 = 26

Now, perform the arithmetic operation in base-10:

23 - 16 + 26 = 33

Finally, convert the result back to base-3. The number 33 can be expressed as 1*(3^3) + 0*(3^2) + 2*(3^1) + 0*(3^0), so 33 in base-10 is (1020)\(_3\).