we know A formula is logically valid (or simply valid) if it is true in every interpretation. These formulas play a role similar to tautologies in propositional logic.
which one could direct me to show the following is valid formula?
$\exists r \forall t A(t,r) \rightarrow \forall t \exists rA(t,r)$
First note that if $\exists r \forall t A(t,r)$ is false in a model, then your statement is true in that model, regardless. Thus we focus only on models where $\exists r \forall t A(t,r)$ is true. What we need to show is that in such models, the statement $\forall t \exists rA(t,r)$ is also true. This follows rather trivially.
The first statement $\exists r \forall t A(t,r)$ is saying that given one single value $r$, no matter what $t$ is, $A(t,r)$ is true. The second statement $\forall t \exists r A(t,r)$ is saying that for any choice of $t$, there exists a value of $r$ in the universe that makes $A(t,r)$ true: ie we can define at least one function that takes possible $t$'s as input and outputs the $r$ that makes $A(t,r)$ true. Since the first statement is true, every model has some constant that works regardless of $t$. Simply choose this constant as the constant function, and you can see why the second statement must be true.