We know that, the equation of normal at the
point $\left(x_{1}, y_{1}\right)$ to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is $\frac{a^{2} x}{x_{1}}+\frac{b^{2} y}{y_{1}}=a^{2}+b^{2}$
Given equation is $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$
Here, $\,\,\,\,\,\,a^{2}=16,\,\, b^{2}=9$
$\therefore \,\,\,$ The equation of normal at the point $(-4,0)$ is
$\frac{16 x}{-4}+\frac{9 y}{0}=16+9$
$\Rightarrow \,\,\,\,\, \frac{9 y}{0}=25+\frac{16 x}{4}$
$\Rightarrow \,\,\,\,\,\,9 y=0 $
$ \Rightarrow \,\,\,\,y=0$