Answer
$y=(x-4)^3$
Work Step by Step
RECALL:
(i)
$y=-f(x)$ involves a reflection about the x-axis of the parent function $y=f(x)$.
(ii)
$y=af(x)$ involves either a vertical compression by a factor of $a$ of the parent function $f(x)$ when $a\gt 1$or a vertical stretch if $0\lt a \lt1$.
(iii)
$y=f(x) + k$ involves either a vertical shift of $k$ units upward of the parent function when $k\gt 0$ or $|k|$ units downward when $k \lt0$.
The function graph involves a 4-unit shift to the right of the parent function.
Thus, the equation of the function is:
$y=f(x-h)^{3}
\\y=(x-4)^3$