Nex 6 dust problem

I have a NEX-7 and it has a cleaning mode and I think the NEX-6 has one too.

Go to setup

Select cleaning mode

press OK

After this you take the lens off and spray the sensor with one of those pump sprayers.  Replace lens and turn camera off.  Check thur view finder for spots and you sensor should be clean until you need to send it in for cleaning.  I hope this helps you.