The ratios wanted are 6:7:1
Add all the numbers together. 6+7+1 = 14. That means that out of every 14 DVDs Arthur would have
6 Comedy DVDs
7 Horror DVDs
1 Documentary DVD ( You missed off one type of DVD)
But Arthur has 98 DVDs. Which is 7 lots of 14. So Arthur's collection is actually
7*6 = 42 Comedy DVDs
7*7 = 49 Horror DVDs
7*1 = 7 Documentary DVDs
DVD Collection: 42 Comedy DVDs, 49 Horror DVDs, 7 Documentary DVDs