I have that 29/35 is painted and 6/35 is left to paint.

I also know that 3 5/12qts were used to paint the 29/35.
But I do not know how to do the work on how much paint will be needed to finish the 6/35 that is left to paint

I would just use a simple ratio.

29/35 : 6/35
= 29 : 6

since 3 5/12 = 41/12

so x/(41/12) = 6/29

29x = 6(41/12) = 41/2
x = 41/58 quarts needed to finish the job