\( \left. \begin{array} { l } { \vec { u } = ( 2 , - 4 ) } \\ { \vec { w } = ( - 6 , - 4 ) } \\ { \frac { 1 } { 2 } \vec { u } + 3 \vec { w } = ( \square , \square ) } \end{array} \right. \)

Let's break it down step by step! First, we calculate \( \frac{1}{2} \vec{u} \). Since \( \vec{u} = (2, -4) \), we have: \[ \frac{1}{2} \vec{u} = \left( \frac{1}{2} \times 2, \frac{1}{2} \times -4 \right) = (1, -2). \] Next, we compute \( 3 \vec{w} \) where \( \vec{w} = (-6, -4) \): \[ 3 \vec{w} = (3 \times -6, 3 \times -4) = (-18, -12). \] Now, we can combine these results: \[ \frac{1}{2} \vec{u} + 3 \vec{w} = (1, -2) + (-18, -12) = (1 - 18, -2 - 12) = (-17, -14). \] So the final answer is: \[ \frac{1}{2} \vec{u} + 3 \vec{w} = (-17, -14). \]