Short Answer 
To derive the transformation logic, first identify how the numbers change, such as doubling and subtracting. For the input (10), using the established pattern, doubling gives (20) and subtracting (2) results in (18). Thus, (10) transforms to (18).
Step 1: Identify the Pattern
Begin by analyzing the transformations of the numbers. Recognize the pattern that emerges from the given pairs by looking at how each first number transitions to its corresponding second number. The steps are:
- For the first pair, (7) becomes (12).
- For the second pair, (20) becomes (38).
- The last pair is (2) which remains (2).
Step 2: Apply the Transformation Logic
Examining how each number changes will help in replicating the method. Specifically, notice how each number is manipulated through doubling and subtraction. This is the procedure you’ll follow:
- For (7), double it to (14) and subtract (2) to get (12).
- For (20), double to get (40) and subtract (2) leading to (38).
- For (2), doubling yields (4), and subtracting (2) results in (2) again.
Step 3: Compute the Final Value
Now that you understand the pattern, apply it to (10) to find its value. Follow the established transformation logic for clarity:
- Start with (10) and double it to get (20).
- Subtract (2) from (20), which results in (18).
- Thus, (10) becomes (18) in this numerical transformation.