Hi,
I can see that you have HikaShop Essential, so you would have to upgrade to the Business edition as the feature you need to do that is only available with the Business edition:
www.hikashop.com/extensions/upgrade-my-version.html
Then, you can go in the menu Display>Custom fields, and create first a custom field of the table "order" and of the type "advanced date picker" that you can configure how you want for the selection of the day. And then, you can create a second custom order field of the type "single dropdown" for the selection of the hour range below the selection of the day. You can enter the ranges you want as values of that second custom field.
The fields will appear on the checkout thanks to the "fields" view in your "checkout workflow", so make sure you didn't remove it from your checkout workflow.