Die Antwort von @SérgioMichels sollte richtig sein. Aber es erhält nicht den Namen des Verkäufers und verwendet eine Syntax, die (meiner Meinung nach) vermieden werden sollte.
Also, hier ist eine Alternative...
SELECT
buyer.name AS buyer,
buyerWants.name AS buyer_wants, (assuming the items have names),
buyerHas.name AS buyer_has,
seller.name AS seller,
sellerWants.name AS seller_wants,
sellerHas.name AS seller_has
FROM
People AS buyer
INNER JOIN
Wishlist AS buyerWants
ON buyerWants.person_id = buyer.person_id
INNER JOIN
Giveaways AS sellerHas
ON sellerHas.item_id = buyerwish.item_id
INNER JOIN
People AS seller
ON seller.person_id = sellerHas.seller_id
INNER JOIN
WishList AS sellerWants
ON sellerWants.person_id = seller.person_id
INNER JOIN
GiveAways AS buyerHas
ON buyerHas.item_id = sellerWants.item_id
AND buyerHas.person_id = buyer.person_id
WHERE
buyer.person_id = ?
