Odpověď @SérgioMichels by měla být správná. Ale nezískává jméno prodejce a používá syntaxi, které je třeba se (podle mého názoru) vyhnout.
Takže tady je alternativa...
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 = ?