The third reasoning step in evaluating the complex number expression $(5 - 4i) - 2(3 + 6i)$ is to perform subtraction on the simplified expression $(5 - 4i) - (6 + 12i)$. This is done by combining the real parts $(5 - 6)$ and the imaginary parts $(-4i - 12i)$, which results in $-1 - 16i$.