problem: $P$ and $Q$ represent numbers, and $P \ast Q$ means $\cfrac{P+Q}{2}$. What is the value of $3 \ast (6 \ast 8)$?
solution: According to the order of operations, first perform the operation indicated in the parentheses.
  
  $6 \ast 8 = \cfrac{6+8}{2}$ or 7. Then $3 \ast (6 \ast 8) = 3 \ast 7 = \cfrac{3+7}{2}$ or $\boxed{5}$.