The maximum number of databases your free hosting account provides is listed on the left side of your website control panel under General Information.

For example:

MySQL Databases 1 / 6
Which means I’m using 1 database out of 6 possible databases.

Don’t confuse this as meaning you can only install 6 scripts which use MySQL, by all means you can install many, many scripts into a single database, even two installations of the same script such as phpBB.

All you need to do is just give each script it’s own table prefix during installation like…

forum1_ for the first installation of phpBB using the same database
forum2_ for the second installation of phpBB using the same database