Please help with this, provide detailed explanation.

DFS $($Depth$-$First Search$)$ with Pre$-$ and Post$-$Numbers: Consider the following directed graph with $8$ nodes: A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ H$.$ The edges are given as follows: $,$ C$),($E$,$ G$),($F$,$ E$),($F$,$ G$),($H$,$ D$),($H$,$ G$).$ Perform a depth$-$first search traversal starting from vertex A and list the order in which the nodes are visited. Additionally, provide the pre$-$number and post$-$number for each node, which represent the clock times in which the nodes are first encountered and fully explored, respectively. Also: identify all tree edges as well as back edges.