14) \( 12\left(\frac{1}{12} y-\frac{1}{4} x-\frac{3}{4} x-\frac{2}{3} y\right) \)

To simplify the expression \( 12\left(\frac{1}{12} y - \frac{1}{4} x - \frac{3}{4} x - \frac{2}{3} y\right) \), we will first simplify the expression inside the parentheses. 1. Combine the terms involving \( y \): \[ \frac{1}{12} y - \frac{2}{3} y \] To combine these, we need a common denominator. The least common multiple of 12 and 3 is 12. We can rewrite \(\frac{2}{3} y\) as: \[ \frac{2}{3} y = \frac{8}{12} y \] Now we can combine: \[ \frac{1}{12} y - \frac{8}{12} y = \frac{1 - 8}{12} y = -\frac{7}{12} y \] 2. Combine the terms involving \( x \): \[ -\frac{1}{4} x - \frac{3}{4} x = -\left(\frac{1}{4} + \frac{3}{4}\right) x = -1 x = -x \] Now we can rewrite the expression inside the parentheses: \[ -\frac{7}{12} y - x \] 3. Now, we multiply the entire expression by 12: \[ 12\left(-\frac{7}{12} y - x\right) \] Distributing the 12: \[ 12 \cdot -\frac{7}{12} y + 12 \cdot -x = -7y - 12x \] Thus, the simplified expression is: \[ \boxed{-7y - 12x} \]