The lowest number of packages of plates Shaniya could buy is 3, because it's the least common multiple of 8 and 6.
8 plates per package,
8 x 3 = 24.
6 Cups per package,
6 x 4 = 24 as well.
So if she bought 3 packages of plates, she could buy 4 packages of cups and have the same amount of each.
Hope this helped!