The syntax for index hints is documented here:
http://dev.mysql.com/doc/refman/5.6/en/index-hints.html
FORCE INDEX goes right after the table reference:
SELECT * FROM (
SELECT owner_id,
product_id,
start_time,
price,
currency,
name,
closed,
active,
approved,
deleted,
creation_in_progress
FROM db_products FORCE INDEX (products_start_time)
ORDER BY start_time DESC
) as resultstable
WHERE resultstable.closed = 0
AND resultstable.active = 1
AND resultstable.approved = 1
AND resultstable.deleted = 0
AND resultstable.creation_in_progress = 0
GROUP BY resultstable.owner_id
ORDER BY start_time DESC
WARNING:
If you're using ORDER BY before GROUP BY to get the latest entry per owner_id, you're using a nonstandard and undocumented behavior of MySQL to do that.
There's no guarantee that it'll continue to work in future versions of MySQL, and the query is likely to be an error in any other RDBMS.
Search the greatest-n-per-group tag for many explanations of better solutions for this type of query.