1. **State the problem:** Simplify the expression $7 - 4 \times (3 - 8) + 2 \times (5 - 9)$.\n\n2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).\n\n3. **Evaluate inside parentheses:**\n$3 - 8 = -5$\n$5 - 9 = -4$\n\n4. **Substitute back:**\n$7 - 4 \times (-5) + 2 \times (-4)$\n\n5. **Multiply:**\n$-4 \times (-5) = 20$\n$2 \times (-4) = -8$\n\n6. **Rewrite expression:**\n$7 + 20 - 8$\n\n7. **Add and subtract from left to right:**\n$7 + 20 = 27$\n$27 - 8 = 19$\n\n**Final answer:** $19$