Here, start with $a$ and end with $f$.
$$a \;\_ \; \_ \; \_ \; \_ \; f$$
Blank spaces are to be filled with $b$, $c$, $d$, $e$ such that $b$ comes before $c$, and $d$ comes before $e$.
Number of ways to arrange $b$, $c$, $d$, $e$ such that $b$ comes before $c$ and $d$ comes before $e$, will be = $4!/(2!*2!) = 6$