One of the goals of the post-9/11 war in afghanistan was to

Defeat the Taliban and al -Qaeda

Explanation:

The Taliban was long thought to have ties to the terrorist group al-Qaeda and provided both funding and served as a sanctuary to the terrorist group.

   To defeat Al-Qaeda and the Taliban

Explanation:  After the 9/11 terrorist attack, US authorities with President Bush were determined to defeat Al-Qaeda and Osama bin-Laden as the organizers of the theoretical attack. Although none of the terrorists involved in the 9/11 attack were from Afghanistan, the Taliban provided support and refuge for Al-Qaeda. President Bush stressed that if the Taliban do not deliver Al-Qaeda leaders, they will face the same fate as Al-Qaeda.