15. Algebra \( A \) system of equations has no solution. One equation is \( y=6 x+4 \) and the other equation is \( y=\frac{a}{2} x-1 \). Find the value of \( a \).

1. Since the system of equations has no solution, the two lines represented by the equations must be parallel. Two lines are parallel if and only if they have the same slope. 2. The first equation is \[ y = 6x + 4. \] Its slope is \(6\). 3. The second equation is \[ y = \frac{a}{2}x - 1. \] Its slope is \(\frac{a}{2}\). 4. For the lines to be parallel, set the slopes equal: \[ 6 = \frac{a}{2}. \] 5. Multiply both sides by \(2\) to solve for \(a\): \[ 2 \times 6 = a, \] \[ a = 12. \] 6. Since the y-intercepts are different (\(4\) in the first equation and \(-1\) in the second), the lines are distinct. Thus, the value of \(a\) that makes the system have no solution is \[ \boxed{12}. \]