Not currently. Airtable forms are pretty bare-bones in terms of logic features, and they don’t check the existing data in the table when a user is filling out the form.
To apply the solution that @Kamille_Parks suggested, create a new [Dates] table, with each record’s primary field containing a unique date. Back in your main table, turn the {Date} field into a link field where users can pick an entry from the [Dates] table, making sure to turn off the “Allow linking to multiple records” feature to prevent multiple dates from being picked.
Back in the [Dates] table, you’ll see that there’s a new link field there as well. That’s the “other side” of the link coming from your main table. To count how many links each date record has, add a count field and name it something like {Responses}.
On that same table, create a new view named something like “Open Dates”, and add a filter to only show records where Responses < 8. That will automatically hide any date records that have eight responses.
In the form view that you made on your main table, edit the properties of the link field to only select records from that “Open Dates” view. Once a date has eight responses, it won’t appear as an option for anyone responding after that.
