Let's simplify and solve the equation step-by-step:
Given: \[ 3x - 2x + 4 = 5x - 4x - 8 \]
First, simplify both sides:
Left side: \[ 3x - 2x + 4 = x + 4 \]
Right side: \[ 5x - 4x - 8 = x - 8 \]
Now, we have: \[ x + 4 = x - 8 \]
Next, subtract \( x \) from both sides: \[ 4 = -8 \]
This statement is false, meaning there are no values of \( x \) that can satisfy the equation.
Thus, the solution is: D: no solution.