Final answer:
Shaniya needs to buy 3 packages of plates.
Step-by-step explanation:
To have the same number of each item, Shaniya needs to find the least common multiple (LCM) of 6 and 8. The LCM of 6 and 8 is 24. This means that Shaniya needs to buy 3 packages of plates in order to have the same number of cups and plates for the party.