There are a few strategies you can use to display this information, but it would likely need to be on the cart template and not on the actual checkout itself. I wouldn't necessarily use a product option to display your bin numbers, but it might be worth investigating metafields to have some discrete information included on your products.
Here's an app that many folks use to include additional information about their products:
Integrating it with your template might be a little tricky though, and so for assistance I might reach out to the Shopify Design Gurus. They're awesome at what they do, and can likely help you out here. You can reach out to them at firstname.lastname@example.org
If you are not using the product sku field (and never will) you'd be able to appropriate that for your use here. Just add the bin# in the sku field and add the code on the product to show it.
Meta-fields does seem like neater way to add such data though. I made a tool that makes adding metafields a little easier than the one posted above, but any of them will do the job you need.
Jason's got a really good point here. If you're physically storing the product in your own warehouse and not using a dropshipping service or something like Shipwire to handle fulfilment, you can probably use the SKU field for each variant.
I should give a shout-out to Jason for his Shopify extensions for Chrome. He does some great work, which you should check out here.
Thank you for the answers, I will definitely check out meta fields and chrome extensions, but I think I did not explain well the second part of my question. I want to see product pictures and bin # on the order details page in admin section, on this page:
this is for the person who fulfills the order. Picture and bin # beside the product will help tremendously, is it doable?
Thanks for clarifying. This currently isn't possible on Shopify, as the order details page does not show the images of the products ordered. However, you could create a similar effect with the new order notification email, which your fulfiller could be subscribed to, or perhaps your fulfilment request email, which you could set up to send to your fulfiller.
I'm fairly certain you could call in the pictures and, let's say, SKU field for your bin numbers, but I think Jason might have a better idea on how to accomplish that.
i put some of the products within tab by sorting also, now i want to modify quantity items and click (save) to the "add to cart" buttton, but the button is not working. how is it working? please reply to as soon as possible. that link is http://myakr-corporation.myshopify.com/