Let $A=(3,-2,2)$
$$
\begin{aligned}
& B=(6,-17,-4) \\
& P=(2,3,4)
\end{aligned}
$$
Let $P$ divides $A B$ in the ratio of $m: n$.
$$
\begin{gathered}
P=\left[\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}, \frac{m z_2+n z_1}{m+n}\right] \\
(2,3,4)=\left[\frac{m(6)+n(3)}{m+n}, \frac{m(-17)+n(-2)}{m+n},\right. \\
(2,3,4)=\left[\frac{6 m(-4)+n(2)}{m+n}\right] \\
\frac{6 m+3 n}{m+n}=2 \\
6 m+3 n=2 m+2 n \\
4 m=-n \\
\frac{m}{n}=-\frac{1}{4} \\
m: n=-1: 4
\end{gathered}
$$
We know that,
If point $P$ divides a line segment in the ratio of $m: n$, then its harmonic conjugate will divide same segment in the ratio of $-m: n$
$\therefore$ Required ratio $=-m: n=1: 4$
$\therefore$ Required harmonic conjugate
$$
\begin{aligned}
& =\left(\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}, \frac{m z_2+n z_1}{m+n}\right) \\
& =\left(\frac{1(6)+4(3)}{1+4}, \frac{1(-17)+4(-2)}{1+4}, \frac{1(-4)+4(2)}{1+4}\right) \\
& =\left(\frac{18}{5}, \frac{-25}{5}, \frac{4}{5}\right)=\left(\frac{18}{5},-5, \frac{4}{5}\right)
\end{aligned}
$$
Hence option (4) is correct.