In the binomial expansion of $(3x - y)^6$, the general term can be expressed as $T_k = \binom{n}{k} (a)^{n-k} (b)^k$, where $n$ is the exponent, $a$ is the first term, and $b$ is the second term. For the fourth term, $k=3$, leading to $T_4 = \binom{6}{3} (3x)^{6-3} (-y)^3$. This simplifies to $-540x^3y^3$, confirming the term's value.