1. **State the problem:** Solve the equation $12c - 4 = 14c - 10$ for $c$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing the same operation on both sides. 3. **Step 1:** Move all terms involving $c$ to one side and constants to the other: $$12c - 4 = 14c - 10$$ Subtract $12c$ from both sides: $$-4 = 14c - 12c - 10$$ Simplify: $$-4 = 2c - 10$$ 4. **Step 2:** Add 10 to both sides to isolate the term with $c$: $$-4 + 10 = 2c - 10 + 10$$ Simplify: $$6 = 2c$$ 5. **Step 3:** Divide both sides by 2 to solve for $c$: $$\frac{6}{2} = \frac{2c}{2}$$ Simplify: $$3 = c$$ 6. **Final answer:** $$c = 3$$ This means the value of $c$ that satisfies the equation is 3.