Answer
-64
Work Step by Step
Based on the quotient rule for exponents, we know that $\frac{a^{m}}{{a}^{n}}=a^{m-n}, a\ne0$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $\frac{(-4)^{6}}{(-4)^{3}}=(-4)^{6-3}=(-4)^{3}=-4\times-4\times-4=-64$.