In forall x: Calgary, by P. D. Magnus, p. 153, there is this question:
B. Formulate strategies for working backward and forward from $\mathcal{A} \leftrightarrow \mathcal{B}$.
Working forward
Having $\mathcal{A} \leftrightarrow \mathcal{B}$ as a premise, I would want to eliminate the biconditional. So, I would need to find A and justify it using a conditional. Then, I could use $\leftrightarrow E$ to get $\mathcal{B}$.
I need to use Elimination Rules when working forward and Introduction Rules, backward.
Is something similar to this what the book asks ? Not sure if he is referring to working forward from premises or $\mathcal{A} \leftrightarrow \mathcal{B}$ is a sentence that appear somewhere in the proof (or subproof).
Yes, that is it. You want strategies that take $A\leftrightarrow B$ as one of the premises, assumptions, or derivations and work forward towards deriving some target.
The rules of biconditional elimination and conditional elimination, along with having one of the equivalents ($A, B$), will build such a strategy.
Likewise you want strategies where $A\leftrightarrow B$ is the target, and work backward to derive that target.