\( \operatorname { gar } : ( 16 b c - 12 c d ) + ( - 8 c d + 6 b c + 4 b d ) \)

First, let's simplify the expression step by step: 1. Start with the original expression: \( (16bc - 12cd) + (-8cd + 6bc + 4bd) \). 2. Combine like terms: - For the \(bc\) terms: \(16bc + 6bc = 22bc\). - For the \(cd\) terms: \(-12cd - 8cd = -20cd\). - The term \(4bd\) stands alone. 3. Now, put it all together: The simplified expression is \( 22bc - 20cd + 4bd \). Simplifying expressions is a handy skill that can help in various areas, including programming, economics, and machine learning, where efficiency and clarity are key! If you ever find yourself confused when combining like terms, remember to group them based on their variable components. It could save you some time and prevent extra mistakes!