The easier way to multiply mixed numbers is to turn them into improper fractions. 6 3/4 as an improper fraction is 27/4, and 3 4/5 as an improper fraction is 20/5. 27/4 x 20/5. There is some cancelling that can be done here, so you divided 20 from 20/5 and 4 from 27/4, which leaves it at 20/1 x 5/5 = 135/5.
Now you're left with a big improper fraction, and this can be simplified. Divide 135 by 5, which is 27. And there you have it. The answer is a whole number. Hope this helps! :)