1. **State the problem:** Simplify the expression $20x - 6y + 2 - 12x + 8y - 10 + 15$. 2. **Group like terms:** Combine the terms with $x$, the terms with $y$, and the constant terms separately. 3. **Combine $x$ terms:** $20x - 12x = 8x$. 4. **Combine $y$ terms:** $-6y + 8y = 2y$. 5. **Combine constants:** $2 - 10 + 15 = 7$. 6. **Write the simplified expression:** $8x + 2y + 7$. **Final answer:** $8x + 2y + 7$