2/9 : (11/18 - 7/10) + 7 * 2 1/14

1. Find a common denominator for the fractions inside the parentheses: 18 and 10. The least common multiple is 90. So, (11/18 - 7/10) = (55/90 - 63/90) = -8/90 = -4/45.

2. Perform the division: 2/9 : (-4/45) = 2/9 * (-45/4) = -90/36 = -5/2.

3. Convert the mixed number to an improper fraction: 2 1/14 = 29/14.

4. Perform the multiplication: 7 * 29/14 = 203/14 = 29/2.

5. Add the results: -5/2 + 29/2 = 24/2 = 12.

Final Answer: 12