How to delete 38,000 emails in mass on Mac but save those received in the past 6 months?

You might try a smart mailbox with criteria like this:

or whatever date fits your requirements. Be sure to check it closely to make sure no newer emails are included.

Then select batches of a couple of thousand at a time and delete and empty trash. Deleting all at once could lock up Mail and/or your Mac.

If the email were in the Trah bin and you closed Mail and then reopened it they would have been deleted if this menu item for your email account Mailbox Behaviors pane in Mail's Settings was selected:

assuming that you have the mail app set to show newest mails at the top:

you can scroll down to the first email among those that you want to delete, you can click on that email. then you scroll down to the last email you wish to delete, and press and hold your "shift" key and click on that email. you should then see ALL of the emails you wish to delete are highlighted. then all you need to do is click your keyboard's delete key.

but you should check the highlighted emails to make sure that you definitely want to delete all those that are highlighted, because there is no "are you sure?" safety net. (although you will find them in your trash)

Old Toad wrote:

Deleting all at once could lock up Mail and/or your Mac.

thanks Old Toad. I was unaware of that.