The problem requires us to determine the remainder when the polynomial function `f(x) = 3x^3 - 27x^2 + 18x - 168` is divided by `(x - 4)`.
The method we are going to use to solve this is known as polynomial division, which is kind of similar to the basic long division we learned in grade school, but applied to polynomial expressions.
Firstly, set `x = 4` in the polynomial function `f(x)` because we are dividing by `(x - 4)`. We do this because according to the Remainder Theorem, the remainder of a polynomial `p(x)` divided by `(x - a)` is equal to `p(a)`.
So, let's substitute `4` into the polynomial function:
`f(4) = 3(4)^3 - 27(4)^2 + 18(4) - 168 = 192 - 432 + 72 - 168 = -336`.
After calculating the above expression, we get `-336`.
Therefore, the remainder when the polynomial `f(x) = 3x^3 - 27x^2 + 18x - 168` is divided by `(x - 4)` is `-336`. This corresponds to none of the given options a, b, c or d.