Once you've downloaded all of the photos from a memory card in your Sony a6000 and saved them in a safe place (with a backup, of course), it's time to delete the photos from the card to free up space for new ones.
While you could, technically, delete them individually use the delete button (trash can icon), that's an awfully slow and tedious way to do it. A much better way--and, as it happens, a safer one, too--is to format the memory card.
On the Sony a6000's menu system on the back screen, you'll find the Format item under page 5 of the tab with the toolbox icon.
Formatting the memory card deletes all the data on it (although it might still be recoverable). So when you click on that option, you'll be asked for confirmation.
It'll then take a few moments to format the card, giving you an orange progress bar.
Once it's done, it'll return you to the main menu automatically.
What to Do if You Accidentally Format Your Memory Card
Despite the extra confirmation step, it can still happen that you realize too late that you didn't really want to format the memory card. In theory, your images are gone. But in practice, it might still be possible to recover them.
The first thing to do is to stop using the memory card. You don't want to be writing anything else to it if you can help it. Then it's time to break out some data recovery software. There are several available, and while they all do similar things, they do it in different ways. Some are free, and some are paid, although many of the paid ones have a trial version that at least allows you to see what's recoverable and then decide whether or not to buy a license so that you can actually do the recovery.
I've put together a roundup of the best software to recover deleted photos here.