1. **State the problem:** Solve the equation $6x - 2x = 32$ for $x$. 2. **Combine like terms:** Since both terms on the left side have $x$, subtract the coefficients: $$6x - 2x = (6 - 2)x = 4x$$ So the equation becomes: $$4x = 32$$ 3. **Isolate $x$:** Divide both sides by 4 to solve for $x$: $$\frac{\cancel{4}x}{\cancel{4}} = \frac{32}{4}$$ 4. **Simplify:** $$x = 8$$ 5. **Answer:** The solution to the equation is $x = 8$.