How many solutions does the equation 4(x-2) = -2(x+4) have? (May 2023 U.S.)

Correct answer: B. Exactly one.
To solve this problem, we need to simplify the equation and then solve for the value of x.
The given equation is:
4(x-2) = -2(x+4)

Simplifying the equation:
4x - 8 = -2x - 8
6x = 0
x = 0

Now, let's check if there are any other solutions.
Substituting x = 0 back into the original equation:
4(0-2) = -2(0+4)
-8 = -8

The equation is satisfied when x = 0.
Therefore, the equation 4(x-2) = -2(x+4) has exactly one solution, which is x = 0.