Place Value Modification: Changing Digits in 429

To solve this problem, we will modify the digits of the number 429 based on the given instructions:

• Step 1: Identify the digits in the number 429. The hundreds digit is 4, the tens digit is 2, and the ones digit is 9.
• Step 2: Increase the tens digit by 1. Therefore, the new tens digit is $2 + 1 = 3$.
• Step 3: Increase the hundreds digit by 2. Therefore, the new hundreds digit is $4 + 2 = 6$.
• Step 4: Construct the new number. The new number has a hundreds digit of 6, a tens digit of 3, and an unchanged ones digit of 9.

Therefore, the new number formed is $639$.

The correct answer to this problem is $639$, which matches choice 2.