  In this paper we completely solve a simple quartic family of Thue equations
over $\mathbb{C}(T)$. Specifically, we apply the ABC-Theorem to find all
solutions $(x,y) \in \mathbb{C}[T] \times \mathbb{C}[T]$ to the set of Thue
equations $F_{\lambda}(X,Y) = \xi$, where $\xi \in \mathbb{C}^{\times}$ and
\begin{equation*} F_{\lambda}(X,Y):=X^4 -\lambda X^3Y -6 X^2Y^2 + \lambda XY^3
+Y^4, \quad \quad \lambda \in \mathbb{C}[T]/\{\mathbb{C}\} \end{equation*}
denotes a family of quartic simple forms.
