The number of spanning trees in a graph $G$ containing an edge $e$ is equal to the number of spanning trees in $G/e$. The number of spanning trees in a graph $G$ not containing an edge $e$ is equal to the number of spanning trees in $G − e$.
I understand $G-e$ will give the number of spanning trees without edge $e$, but how come $G/e$ will have the same number of spanning trees as graph $G$?
$G/e$ doesn’t have the same number of spanning trees as $G$; that’s not what it says. The number of spanning trees of $G/e$ is the same as the number of spanning trees of $G$ that contain the edge $e$. And that’s easy to see: if you have a spanning tree of $G$ that contains $e$, just collapse $e$ to form $G/e$, and you have a spanning tree of $G/e$.