use sed or grep?

Shell Programming and Scripting
1

Hello,
I have variable and I need to get few characters from that path of the directory:
Example:

 
set A = /a/b/c/d/e/f
My Code:
echo $A | sed 's/.*\(.*\).*b/\1/'
O/P:
/c/d/e/f

Instead I want a one liner preferably the same logic using sed (ease of understanding), to get just the "c" that is anything after b between (backslahes) /?/, which in this case is c.
Thanks

2 
 echo "$A" | cut -d/ -f4
3

Can you please elaborate on this?

4 
echo "$A" | cut -d/ -f4

-d is deliminator which is "/"
-f is the field number c is the 4th field.