To simplify the expression \( 3(42 + 32 \div 4 - 5) \), you first need to focus on the part inside the parentheses: \( 42 + 32 \div 4 - 5 \).
In this part, the division operation \( 32 \div 4 \) needs to be calculated first, according to the order of operations (PEMDAS/BODMAS).
So, the quotient that must be found to simplify the expression is \( 32 \div 4 \).
Thus, the answer is \( 32 \div 4 \).