To simplify the expression \(3(42 + 32 \div 4 - 5)\), we first need to determine which quotient is necessary to simplify the expression inside the parentheses.
The expression inside the parentheses is \(42 + 32 \div 4 - 5\). The first operation we need to perform according to the order of operations (PEMDAS/BODMAS) is the division \(32 \div 4\).
Thus, the quotient we need to find to simplify the expression is \(32 \div 4\).
So, the correct response is: 32 ÷ 4.