Solve the equation, and check your solution. \[ 12 x-4(x-6)=8 x+4 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). (Simplify your answer.) B. The solution set is \{all real numbers\}. C. The solution set is \( \varnothing \).

Given the equation: \[ 12x - 4(x-6) = 8x + 4 \] **Step 1: Distribute \(-4\) on the left-hand side.** \[ 12x - 4x + 24 = 8x + 4 \] **Step 2: Combine like terms.** \[ (12x - 4x) + 24 = 8x + 4 \quad \Longrightarrow \quad 8x + 24 = 8x + 4 \] **Step 3: Subtract \(8x\) from both sides to isolate the constant terms.** \[ 8x + 24 - 8x = 8x + 4 - 8x \quad \Longrightarrow \quad 24 = 4 \] Since \(24\) does not equal \(4\), a contradiction occurs, indicating that no value of \(x\) satisfies the equation. **Conclusion:** The solution set is the empty set. C. The solution set is \(\varnothing\).