How many real solutions does the equation |3x - 6| = 2x have?

Split the absolute value equation into two cases. Case 1: $3x - 6 = 2x$ gives $x = 6$. Case 2: $3x - 6 = -2x$ gives $5x = 6$ and $x = \frac{6}{5}$. Because $|3x-6|$ cannot be negative, the right side $2x$ must be nonnegative, so $x \geq 0$. Both solutions satisfy that. Check $x = 6$: $|12| = 12 = 2(6)$. Check $x = \frac{6}{5}$: $|3.6 - 6| = 2.4 = 2(1.2)$. So there are 2 real solutions, choice A. Choice B (0) and choice C (1) miss a valid case, and choice D is impossible for a linear absolute value equation.