1. **State the problem:** Solve the linear equation $3x - 6 = 2x - 2$ for $x$. 2. **Write down the equation:** $$3x - 6 = 2x - 2$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$3x - 2x - 6 = 2x - 2x - 2$$ $$\cancel{3x} - \cancel{2x} - 6 = \cancel{2x} - \cancel{2x} - 2$$ $$x - 6 = -2$$ 4. **Isolate $x$ by adding 6 to both sides:** $$x - 6 + 6 = -2 + 6$$ $$x = 4$$ 5. **Final answer:** $$x = 4$$ This means the value of $x$ that satisfies the equation is 4.