An equivalence relation $\mathscr{R}$ defined on a set $A = \{a,b,c,d\}$ contains the pairs $(a, a), (a, d), (d, b)$.
In my work below: am I going in the correct direction or am I way off on what is being asked?
\begin{align*} A \times A &= \{a,b,c,d\}\times\{a,b,c,d\}\\ &=[(a,d),(a,b),(a,c),(a,d), \dots] \end{align*}
\begin{align*} A \rightarrow D \rightarrow B \leftarrow A \\ B \rightarrow D \rightarrow A \leftarrow B \end{align*}
You seem to have the right idea in your image, but not in your comment. A correct answer to this question would be $$ \mathscr R = \\ \{(a,a),(a,b),(a,d)\\ (b,a),(b,b),(b,d)\\ \qquad \quad (d,a),(d,b),(d,d),(c,c)\} $$ Note, for instance, that $(a,c) \notin \mathscr R$, just as there is no arrow in your diagram from $A$ to $C$.