1. State the problem: Solve for $y$ in the equation $7y + 15 = 4y - 6$. 2. Subtract $4y$ from both sides to get all $y$ terms on one side: $$7y - 4y + 15 = 4y - 4y - 6 \\ 3y + 15 = -6$$ 3. Subtract 15 from both sides to isolate the term with $y$: $$3y + 15 - 15 = -6 - 15 \\ 3y = -21$$ 4. Divide both sides by 3 to solve for $y$: $$y = \frac{-21}{3} = -7$$ 5. Final answer: $$y = -7$$