Hi there, @AlesiaIleana. Thanks for taking the time to post in the Shopify Community regarding your shipping situation. It's nice to meet you!
I appreciate you sharing the info you did regarding how you set up your rates. If you've removed all of your other rates, created free ones, and this rate is still appearing for your mug, then this indicates that the mug product is likely in a different shipping profile that still has a paid rate within it. You've likely gone ahead and changed the rates for the zones in your General Shipping Profile, but you also likely have a Customer Shipping Profile that appears below your General Profile that houses the mug.
We can check this by going to 'Settings > Shipping and Delivery' and looking for sections that appear like what I show in my screenshot below.
Keep in mind that this is a screenshot from my own store, so if you have any custom shipping profiles, they may be named differently. If you see that you have some custom shipping profiles, click into them, and you should see the products included in them. Once you've found the one with the mug, you should be able to change the rates there, and then you can view how the shipping rates appear in your checkout again.
Follow up with me here once you've given things a second look. I'll keep my eyes peeled for your reply.
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