I'd look here:
SELECT
name
FROM
vendor
WHERE
bom_item.vendor_key =
(
SELECT
vendor_key
FROM
mfg_vendor_relationship
WHERE
bom_item.mfg_key = mfg_key
AND
prefered = TRUE
AND
bom_item.project_key = project_key
)
--
Angular momentum makes the world go ‘round.
You might get away with adding
group by vendor_key
if it turns out you’re simply getting many copies of vendor key from that inner select.
Run it alone to see.