We must remember that a ream is the same of 500 paper sheet.
So, 5 reams means that we have 5 x 500 = 2,500 printer paper sheet every 2 weeks.
If we have 6 cases of premier paper we'll get 6 x 8 = 48 reams of paper.
That means there are 48 x 500 = 24,000 paper sheet.
2,500 paper sheet ------------- 2 weeks
24,000 paper sheet ----------- y weeks
2,500y = 2 x 24,000
2,500y = 48,000
y = 48,000 / 2,500
y = 19 weeks
So, 6 cases of premier paper will last 19 weeks. That's our final answer.