Find the value of the expression \( (4 x-12)+\left(\frac{1}{2} x y-10\right) \) for \( x=4 \) and \( y=6 \). 4 6 8 2

To evaluate the expression \( (4x - 12) + \left(\frac{1}{2}xy - 10\right) \) for \( x = 4 \) and \( y = 6 \), follow these steps: 1. **Substitute the values of \( x \) and \( y \) into the expression:** \[ (4 \times 4 - 12) + \left(\frac{1}{2} \times 4 \times 6 - 10\right) \] 2. **Calculate each part separately:** - **First part:** \[ 4 \times 4 = 16 \] \[ 16 - 12 = 4 \] - **Second part:** \[ \frac{1}{2} \times 4 = 2 \] \[ 2 \times 6 = 12 \] \[ 12 - 10 = 2 \] 3. **Add the results of both parts:** \[ 4 + 2 = 6 \] **Therefore, the value of the expression is \( \boxed{6} \).**