The following system has no solution?
\[
\begin{array}{l}
4 x+6 y=12 \\
6 x+9 y=12
\end{array}
\]

Step 1 ：We are given the system of equations: \[\begin{array}{l} 4x+6y=12 \\ 6x+9y=12 \end{array}\]

Step 2 ：We can determine if the system has a solution by using the concept of determinants. If the determinant of the coefficients of the variables is zero, then the system has no unique solution.

Step 3 ：The determinant of a 2x2 matrix is calculated as follows: \[\text{det} = a*d - b*c\] where a, b, c, d are the coefficients of the variables in the system of equations. In this case, a = 4, b = 6, c = 6, d = 9.

Step 4 ：Substituting the values into the determinant formula, we get: \[\text{det} = 4*9 - 6*6 = 0\]

Step 5 ：The determinant of the coefficients of the variables in the system of equations is zero. This means that the system of equations has no unique solution. However, we also need to check if the system has no solution at all or if it has infinitely many solutions.

Step 6 ：This can be done by comparing the ratios of the coefficients of the variables to the constants. If the ratios are equal, then the system has infinitely many solutions. If the ratios are not equal, then the system has no solution.

Step 7 ：The ratios of the coefficients of the variables to the constants are equal. This means that the system of equations has infinitely many solutions, not no solution.

Step 8 ：Final Answer: The system of equations does not have no solution, it has infinitely many solutions. Therefore, the answer is \(\boxed{\text{False}}\).