MOSFET small signal model output resistance
I think the stated solution has a typo. By inspection, the solution should be

$$
R_{OUT} = (R_{DS} + R4)\;||\;R3
$$

where \$R_{DS}\$ is the FET's drain-to-source resistance, i.e.,

$$
\begin{align*}
R_{DS} &amp;= V_{DS} / I_{DS}\\
&amp;= \frac{V_{DS}}{g_m \cdot V_{GS} + V_{DS}/r_d}\\
&amp;= \frac{V_{DS} \cdot r_d}{V_{DS} + V_{GS} \cdot g_m \cdot r_d}
\end{align*}
$$