At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12. for her party, arpitha purchased the minimum number of hot dog packages and bun packages that she could while making sure to have the same number of hot dogs and buns. how many hot dogs can arpitha serve at her party?

Let's first analyze the word problem we have here.

It is stating that she, Arpitha, bought the MINIMUM packs of hotdogs AND minimum packs of buns to get an equal number of buns to hotdogs.

We can find the multiples they have in common. 

8, 16, 24, 32, 40

12, 24, 36, 48, 60

They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.

Hope this helped!