I believe this should do it for you
select count(c.rf_card_id) as num_card, c.account_id, u.firstname, u.lastname
from rf_card as c
INNER JOIN user_person as u ON c.account_id = u.account_id
INNER JOIN trashes as t ON c.rf_card_id = t.rf_card_id
WHERE date_trunc('day',t.date) between date_trunc('day', DATE '7/01/2010') AND date_trunc('day', DATE '7/15/2010')
group by c.account_id