1. **State the problem:** We are given the equation $2x - (6x - 8) = 32$ and asked to find the value of $8x + 4$. 2. **Rewrite the equation and simplify:** $$2x - (6x - 8) = 32$$ Distribute the minus sign inside the parentheses: $$2x - 6x + 8 = 32$$ 3. **Combine like terms:** $$ (2x - 6x) + 8 = 32$$ $$-4x + 8 = 32$$ 4. **Isolate the variable term:** Subtract 8 from both sides: $$-4x + 8 - 8 = 32 - 8$$ $$-4x = 24$$ 5. **Solve for $x$:** Divide both sides by $-4$: $$x = \frac{24}{\cancel{-4}} \times \frac{\cancel{-1}}{1} = -6$$ 6. **Find the value of $8x + 4$:** Substitute $x = -6$: $$8(-6) + 4 = -48 + 4 = -44$$ **Final answer:** $$\boxed{-44}$$