1. **State the problem:** Simplify and solve the equation $12s - 4s + 2 = 10$ for $s$. 2. **Combine like terms:** The terms $12s$ and $-4s$ are like terms because they both contain $s$. Combine them: $$12s - 4s = (\cancel{12} - \cancel{4})s = 8s$$ So the equation becomes: $$8s + 2 = 10$$ 3. **Isolate the variable term:** Subtract 2 from both sides to isolate the term with $s$: $$8s + 2 - 2 = 10 - 2$$ $$8s = 8$$ 4. **Solve for $s$:** Divide both sides by 8 to solve for $s$: $$\frac{8s}{\cancel{8}} = \frac{8}{\cancel{8}}$$ $$s = 1$$ 5. **Final answer:** The solution to the equation is $s = 1$.