Given equation of parabola is
$y^{2}=64 x\,\,\,...(i)$
The point at which the tangent to the curve is parallel to the line is the nearest point on the curve.
On differentiating both sides of Eq. (i), we get
$2 y \frac{d y}{d x} =64$
$\Rightarrow \frac{d y}{d x} =\frac{32}{y}$
Also, slope of the given line is $-\frac{4}{3}$.
$\therefore -\frac{4}{3}=\frac{32}{y} $
$\Rightarrow y=-24$
From Eq. (i), $(-24)^{2}=64 x$
$ \Rightarrow x=9$
$\therefore $ Hence, the required point is $(9,-24) .$