Maybe it's just called "bitcoin" instead of "bitcoin-qt" on your system (I'm using slightly different version numbers).
no is not working
different version of bitcoin core?
Check the directory for the executable and run it using:
./NAME -datadir=...
Replace
NAME with the name of the executable and
... with the path you want to use (e.g. the one proposed by LoyceV to test).
Regarding your issue.. it definitely seems like a permission issue or a bug.
How did you install core ?
Did you already try to start it via the console and giving it the datadir path via the parameter (i guess you didn't yet?) You might want to try that out.
Also could you give us the output of the directory you are trying to use (using
ls -al inside of
/media/asus/multimedia) ?
Btw, how is your external drive formatted ? Which format did you use ?