  The Hankel determinant $H_{2,2}(F_{f}/2)$ is defined as: \begin{align*}
  H_{2,2}(F_{f}/2):= \begin{vmatrix}
  \gamma_2 & \gamma_3
  \gamma_3 & \gamma_4
  \end{vmatrix}, \end{align*} where $\gamma_2, \gamma_3,$ and $\gamma_4$ are
the second, third, and fourth logarithmic coefficients of functions belonging
to the class $\mathcal{S}$ of normalized univalent functions. In this article,
we establish sharp inequalities $|H_{2,2}(F_{f}/2)|\leq (1272 +
113\sqrt{678})/32856$ and $|H_{2,2}(F_{f}/2)| \leq 13/1080$ for the logarithmic
coefficients of starlike and convex functions with respect to symmetric points.
Moreover, we provide examples that demonstrate the strict inequality holds.
