Aparty store sells large plates in packs of 12 and small plates in packs of 8 . in order to have an equal number of both , what is the least amount of large plants that would have to be purchased

In order to have the least amount of each, you would need to purchase 2 packages of large plates.  Here is the reasoning:

You can buy the following number of large plates and small plates:

Small:  8, 16, 24, 32, ...
Large:  12, 24, 36, ...

The smallest number that can be bought so you have an equal amount is 24 of each.

To get 24 large plates, you would need 2 packages.