Suppose $p,q,r,$ and $s$ are specific statements (arrow means implication).
If I'm asked to prove that $(p\rightarrow q)\rightarrow(r\rightarrow s)$ for those specific $p, q, r,$ and $s,$ how would I set up a proof of that?
Where should we start with and how does natural direction algorithm or truth table shed light on the proof strategies? (or to simplify the statement)
I'm assuming that $p, q, r,$ and $s$ here represent specific statements that you haven't spelled out for us, and that you're asking how to try to organize a proof of $(p\rightarrow q)\rightarrow(r\rightarrow s).$
Typically one would think of this in the equivalent form
$$\big((p\rightarrow q)\wedge r\big)\rightarrow s.$$
One would then assume both $p \rightarrow q$ and $r$ as given, and try to prove $s.$
Alternatively, for a proof by contradiction, you could assume the three statements $\;p \rightarrow q,$ $\;r,\;$ and $\;\lnot s,$ and derive a contradiction.