Hank here from Shopify.
Thank you for the screenshot it really lets me know the steps you have taken with trying to connect your third-party domain.
It looks like you just need to update your DNS settings on your domain website, before trying to verify your domain. Luckily we have an awesome guide that talks you through the steps you need here. I will also share a screenshot of the two bits of information that are crucial to the connection below.
It is very important that you only have one A record in your DNS settings that has a value of 220.127.116.11. And the Cname record should read shops.myshopify.com. Once you have this information in your DNS settings, simply verify the connection once more in Online Store > Domains > Connect a domain.
Let me know how you get on, or if you have any further questions for me!
All the best,