If 4 × 3 = 14, 5 × 4 = 18 and 6 × 5 = 22 under a certain pattern, then what is the value of 7 × 6 following the same rule?

Introduction / Context:
This is a number pattern question where the symbol × does not represent ordinary multiplication. Instead, it denotes a special rule illustrated by the first three examples. After identifying this rule, you are asked to apply it to a new pair of numbers. Such questions check pattern recognition and basic arithmetic reasoning.

Given Data / Assumptions:

- 4 × 3 = 14.
- 5 × 4 = 18.
- 6 × 5 = 22.
- We are asked to find 7 × 6 under the same pattern.
- The symbol × indicates a custom operation, not the usual product.

Concept / Approach:
Observe the relation between the numbers on the left and the results on the right. One simple and consistent pattern is:
Result = 2 × (first number + second number). If this holds for all the given examples, we can confidently apply it to 7 and 6. The pattern is simple and uses only basic addition and multiplication by 2.

Step-by-Step Solution:
Check the pattern for 4 × 3. First number = 4, second number = 3. Compute the sum: 4 + 3 = 7. Multiply by 2: 2 × 7 = 14, which matches the given result. Check the pattern for 5 × 4. First number = 5, second number = 4. 5 + 4 = 9. 2 × 9 = 18, which matches the second result. Check the pattern for 6 × 5. First number = 6, second number = 5. 6 + 5 = 11. 2 × 11 = 22, which matches the third result. Apply the same rule to 7 × 6. 7 + 6 = 13. 2 × 13 = 26.

Verification / Alternative check:
Since the same simple rule works perfectly for all three given examples, it is reasonable to trust that it is the intended pattern. More complicated patterns would be unnecessary. The computed value 26 is present among the options, reinforcing that this interpretation is correct.

Why Other Options Are Wrong:

- 20, 30, and 42 do not equal 2 × (7 + 6) and have no natural connection to the established rule.
- To obtain those values, one would have to change the pattern or apply inconsistent operations, which would contradict the examples provided.

Thus, they cannot be the correct continuation of the pattern.

Common Pitfalls:
Sometimes students may try to involve actual multiplication 4 × 3 = 12 and then add or subtract small adjustments without checking consistency across all examples. Another mistake is to invent a complicated rule when a very simple one, like doubling the sum, fits all cases. Always verify any proposed rule against every given example.

Final Answer:
Using the pattern Result = 2 × (first + second), the value of 7 × 6 is 26.