SELECT
Things_in_boxes.*
FROM
Houses
JOIN Boxes ON Houses.HouseID = Boxes.House
JOIN Things_in_boxes ON Boxes.BoxID = Things_in_boxes.Box
WHERE
Houses.Owner = 'Peter' OR Houses.Owner = 'Paul'
As for resources to learn from... I can't really suggest anything specific. I learnt how to use (My)SQL gradually and from a number of sources, and can't single any of them out as having been of primary importance. w3schools has OK coverage of the very basic stuff, and MySQL's own documentation (available on the web, google for it) does an OK job and is a reasonable reference for when you want to know the nitty gritty of some topic or other.
EDIT: The above answer is wrong. I had missed the stipulation that a House can have multiple Owners.
New approach: I'll assume that there is a cross-referencing table, HouseOwners, with House and Owner as foreign keys.
My first thought was this:
SELECT
Things_in_boxes.*
FROM
Houses
JOIN Boxes ON Houses.HouseID = Boxes.House
JOIN Things_in_boxes ON Boxes.BoxID = Things_in_boxes.Box
JOIN HouseOwners ON Houses.HouseID = HouseOwners.House
WHERE
HouseOwners.Owner = 'Peter' OR HouseOwners.Owner = 'Paul'
However, this is not quite right. If both Peter and Paul are Owners of a given house, then the things in the boxes in that house would show up twice. I think a subquery is needed.
SELECT
Things_in_boxes.*
FROM
Houses
JOIN Boxes ON Houses.HouseID = Boxes.House
JOIN Things_in_boxes ON Boxes.BoxID = Things_in_boxes.Box
WHERE
Houses.HouseID IN (
SELECT DISTINCT House
FROM HouseOwners
WHERE Owner = 'Peter' OR Owner = 'Paul'
) AS MySubquery