1. **State the problem:** Calculate the value of the expression $15 + 6 \div (7 - 14)$. 2. **Recall the order of operations:** Use PEMDAS/BODMAS rules: Parentheses first, then Division, then Addition. 3. **Evaluate inside the parentheses:** $$7 - 14 = -7$$ 4. **Rewrite the expression:** $$15 + 6 \div (-7)$$ 5. **Perform the division:** $$6 \div (-7) = \frac{6}{-7} = -\frac{6}{7}$$ 6. **Rewrite the expression:** $$15 - \frac{6}{7}$$ 7. **Convert 15 to a fraction with denominator 7:** $$15 = \frac{15 \times 7}{7} = \frac{105}{7}$$ 8. **Subtract the fractions:** $$\frac{105}{7} - \frac{6}{7} = \frac{105 - 6}{7} = \frac{99}{7}$$ 9. **Final answer:** $$\boxed{\frac{99}{7}}$$ or approximately 14.1429.