1. **State the problem:** Solve for $y$ in the equation $$7(y - 9) - 2 = -7(-4y + 7) - 9y.$$\n\n2. **Apply the distributive property:** Multiply out the parentheses on both sides.\n$$7y - 63 - 2 = 28y - 49 - 9y$$\n\n3. **Simplify both sides:** Combine like terms.\n$$7y - 65 = 19y - 49$$\n\n4. **Isolate variable terms on one side:** Subtract $7y$ from both sides.\n$$\cancel{7y} - 65 = 19y - 7y - 49 \Rightarrow -65 = 12y - 49$$\n\n5. **Isolate constant terms on the other side:** Add $49$ to both sides.\n$$-65 + 49 = 12y - 49 + 49 \Rightarrow -16 = 12y$$\n\n6. **Solve for $y$ by dividing both sides by 12:**\n$$\frac{-16}{\cancel{12}} = \frac{12y}{\cancel{12}} \Rightarrow y = -\frac{16}{12}$$\n\n7. **Simplify the fraction:** Divide numerator and denominator by 4.\n$$y = -\frac{\cancel{16}^4}{\cancel{12}^4} = -\frac{4}{3}$$\n\n**Final answer:** $$y = -\frac{4}{3}.$$