Enable product packaging option from settings > sales
Post that you can define a pack of 6 and assign it to product Inventory > configuration > product packaging
I see what you are saying, a package can have its own barcode would you know if a package is added to an order by scanning barcode?
For price you can define a promotion or in pricelist
The other possible options which largely depends the inventory management of these products/ packs are
a. Define pack as Product variant, you can provide additional price
b. Define the package as an independent product