you need to join the table to itself for both the myspace and facebook options:
create table MyFavs__APP (
secret_identifier int,
app varchar(16)
);
insert into MyFavs__APP (secret_identifier, app) values
(1, 'facebook'),
(1, 'myspace'),
(2, 'facebook'),
(3, 'myspace'),
(4, 'myspace'),
(4, 'facebook');
select distinct favs.secret_identifier
from MyFavs__APP favs,
MyFavs__APP m,
MyFavs__APP f
where favs.secret_identifier = m.secret_identifier
and favs.secret_identifier = f.secret_identifier
and m.app = 'myspace'
and f.app = 'facebook';
+-------------------+
| secret_identifier |
+-------------------+
| 1 |
| 4 |
+-------------------+
2 rows in set (0.00 sec)