Assalamualaykum, Excuse the explicit language but If Mathi comes out, Is it mandatory to wash the entire private part including the testicles. Or only the area from where Mathi came out? JazakAllah Khair.

Ustadh AbdulAziz al-Haqqan
This is the Hadith of the Messenger (sallallahu alayhi wa sallam). However, some of the people of Ilm said this is just a favor to do, and some said it is because it remedies it; that's why the Messenger said it. Our Sheikh Muhammad Hisham says the correct opinion is that it may not be impure; however, the vast majority hold that it is impure.