This is what I have so far I just don't know if I am on the right path since I can't seem o piece the last step together.
Let $(a,d)$ be an arbitrary element in $T \circ (S \circ R)$. By existential instantiation $(a,c) \in (S \circ R)$ and $(c,d) \in T$. Once again by existential instantiation we get $(a,b) \in R$ and $(b,c) \in S$. From $(b,c) \in S$ and $(c,d) \in T$, it follows that $(b,d) \in T \circ S$
This is where I am stuck. How do I tie in the fact that $(a,b) \in R$ to get the right hand side?
Just noticed we can finalize the proof, by saying that since $(a,b) \in R$ and $(b,d) \in T \circ S$, we can conclude that $(a,d) \in (T \circ S) \circ R$