Uma simples subconsulta deve fazê-lo bem;
SELECT * FROM food_brands WHERE type_id=
(SELECT MAX(t.id) tid FROM types t
JOIN foods f ON f.id=t.food_id AND f.entry_id=12230)
Um SQLfiddle para testar .
SELECT * FROM food_brands WHERE type_id=
(SELECT MAX(t.id) tid FROM types t
JOIN foods f ON f.id=t.food_id AND f.entry_id=12230)
