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How echo ${instance##*/} expand by shell?

Hello, I am trying to understand following in bash scripts

[user@hostname]$ ls -ld /opt/product/jms/instances/etc/ac4-*
drwxr-xr-x  2 user company 4096 Oct 15 17:18 /opt/product/jms/instances/etc/ac4-sfae-dev
drwxr-xr-x  2 user company 4096 Oct 10 21:08 /opt/product/jms/instances/etc/ac4-sfae-prod
drwxr-xr-x  2 user company 4096 Oct 15 17:09 /opt/product/jms/instances/etc/ac4-sfae-stage
[user@hostname]$ for instance in /opt/product/jms/instances/etc/ac4-*; do echo ${instance##*/}; done

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here I would like to understand how ${instance##*/} is being expanded. I was thinking to use 'basename' but ${instance##*/} also serve my purpose. Though this is the first time I saw this variable so interested to know how does it work. Thanks!
2 Solutions
The word (*/ in this case) is expanded to produce a pattern. If the pattern matches the beginning of the expanded value of parameter, then the result of the expansion is the expanded value of parameter with the longest matching pattern (the ‘##’ case) deleted.
(Therefore the whole path including the last / was deleted and leaving only the file names.)

Refer to http://www.gnu.org/s/bash/manual/bash.html for more details about bash commands.
# means cut from the left side (first instance)
% means cut from the right side (first instance)
## cut from left side but the last instance
%% cut from left side but the last instance

Now say
> a='/opt/product/jms/instances/etc/ac4-sfae-dev'
> echo ${a#*/}              ---- Chops off the first instance of / and the rest is printed.

> echo ${a##*/}    --matches any characters * and then should also match slash, all the match is chopped off from the left side

Now lets chop off the first instance of / from the right side.
> echo ${a%/*}

And the last instance of / from the right side
> echo ${a%%/*}
       NO OUTPUT --everything deleted.

Now suppose we had
> echo ${b%%/*}


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