Offering is a keyword ability.
It is a static ability that allows you to cast a spell with offering for cheaper and at instant speed. To do this, you must sacrifice a creature of a specific subtype and then pay the difference between the spell's mana cost and the sacrificed creature's mana cost.
At the end of Neil's turn, Allison wants to cast a Patron of the Nezumi and controls a Nezumi Cutthroat. As Nezumi Cutthroat is a Rat, she cab sacrifice it and then pay the difference between their mana costs to cast it. The to work out the difference, she must take Patron of the Nezumi's mana cost, , and take from it Nezumi Cutthroat's, . She will thus have to pay .
- 702.47a. Offering is a static ability of a card that functions in any zone from which the card can be cast. "[Subtype] offering" means "You may cast this card any time you could cast an instant by sacrificing a [subtype] permanent. If you do, the total cost to cast this card is reduced by the sacrificed permanent's mana cost."
- 702.47b. The permanent is sacrificed at the same time the spell is announced (see rule 601.2a). The total cost of the spell is reduced by the sacrificed permanent's mana cost (see rule 601.2e).
- 702.47c. Generic mana in the sacrificed permanent's mana cost reduces generic mana in the total cost to cast the card with offering. Colored mana in the sacrificed permanent's mana cost reduces mana of the same color in the total cost to cast the card with offering. Colored mana in the sacrificed permanent's mana cost that doesn't match colored mana in the colored mana cost of the card with offering, or is in excess of the card's colored mana cost, reduces that much generic mana in the total cost.