You "discover" when you finish the process of revealing cards, exiling an appropriate nonland card, casting that card or putting it into your hand, and putting the remaining exiled cards on the bottom of your library in a random order, even if one or more of those actions were impossible for some reason.

You exile the cards face up. All players will be able to see them.

The mana value of a split card is determined by the combined mana cost of its two halves. If discover allows you to cast a split card, you may cast either half (as long as its mana value is less than or equal to the effect's discover value) but not both halves.

If you can't cast the discovered card (perhaps because there are no legal targets for the spell), you'll put it into your hand.

Some spells and abilities that cause you to discover may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won't resolve and you won't discover.

If you cast a spell "without paying its mana cost", you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the spell has any mandatory additional costs, you must pay those to cast it.

If you discover an adventurer card, split card, or modal double-faced card, you might be able to cast that card with either set of characteristics depending on the effect's discover value. For example, if you discover 4 and reveal Galvanic Giant (an adventurer card from Wilds of Eldraine with a mana value of 4), you could cast Galvanic Giant, but not Storm Reading (its Adventure, which has a mana value of 7). If you discover 7 and reveal Galvanic Giant, you could cast either Galvanic Giant or Storm Reading.

When you discover, you must exile cards. The only optional part of the ability is whether you cast the exiled card or put it into your hand.

If the discovered card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

A spell's mana value is determined only by its mana cost. Ignore any alternative costs, additional costs, cost increases, or cost reductions.