Let the total effort required to paint be P.
Tom does P/8 work in an hour
Let Vivian take x hours to paint alone.
So in one hour, Vivian does P/x of the work
Working together, in one hour they do P/6 of the work (since they complete P in 6 hours)

Which gives the equation:


or (since P cancels out)


Simplifying by multipling by 24*x throughout

 or 

So working alone, Vivian would take  hours to paint the house.

Hope this helps!