It's not actually possible to have the checklist show on the front of the card (what you see when looking at the board), only on the card back (what you see when you click a card).
This would be a good suggestion to submit to Trello at firstname.lastname@example.org for future consideration.
There isn't a vanilla Trello solution to this, but there are Chrome Extensions out there that can do this: https://chrome.google.com/webstore/detail/next-step-for-trello/iajhmklhilkjgabejjemfbhmclgnmamf?hl=en
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