To simplify the expression \( 3(42 + 32 \div 4 - 5) \), we need to focus on the division part of the expression, which is \( 32 \div 4 \).
Calculating \( 32 \div 4 \) gives us 8, and that value is then substituted back into the expression.
Thus, the quotient that must be found to simplify the expression is:
32 ÷ 4.