How do I display a fixed size Views grid regardless of the number of results?
You can take a look at Views responsive grid.  I'd suggest using it over the built in views grid because it splits up your rows/columns in a more manageable way.

The functionality you're looking for is built into views, under pager.  You would need to set it to use a pager as well as display 6 results.





The section under Advanced -> No results behavior is what you are looking for.