Solve the equation please show the process to solve

To solve the equation \(3(4x + 8) = 4(3x + 6)\), we will first distribute the constants on both sides.

1. Distribute on both sides: \[ 3(4x) + 3(8) = 4(3x) + 4(6) \] This simplifies to: \[ 12x + 24 = 12x + 24 \]

2. Rearrange the equation: Next, we can subtract \(12x\) from both sides: \[ 12x + 24 - 12x = 12x + 24 - 12x \] This yields: \[ 24 = 24 \]

3. Analyze the result: Since \(24 = 24\) is a true statement, it means that the original equation holds for all values of \(x\). Therefore, there are infinitely many solutions.

To summarize, the equation has infinite solutions.

Answer

The number of solutions to the equation is: infinite.