To solve the equation 4x + 6 = 2(2x + 3), we first distribute the 2 on the right side, which gives us 4x + 6 = 4x + 6. Next, we subtract 4x from both sides, resulting in 6 = 6. This statement is always true, indicating that the original equation does not restrict the value of x. Therefore, any value of x will satisfy the equation, leading to the conclusion that there are infinitely many solutions.