1. **State the problem:** Solve the equation $$5y + 6 = 8y - 12$$ and check the solution. 2. **Write down the formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation by performing inverse operations and maintaining equality. 3. **Step 1: Move all terms involving $y$ to one side.** Subtract $5y$ from both sides: $$5y + 6 - \cancel{5y} = 8y - 12 - \cancel{5y}$$ which simplifies to $$6 = 3y - 12$$ 4. **Step 2: Move constant terms to the other side.** Add $12$ to both sides: $$6 + 12 = 3y - 12 + 12$$ which simplifies to $$18 = 3y$$ 5. **Step 3: Solve for $y$ by dividing both sides by 3:** $$\frac{18}{\cancel{3}} = \frac{3y}{\cancel{3}}$$ which simplifies to $$6 = y$$ 6. **Check the solution:** Substitute $y=6$ back into the original equation: $$5(6) + 6 = 8(6) - 12$$ $$30 + 6 = 48 - 12$$ $$36 = 36$$ The equation holds true, so $y=6$ is the correct solution.