Explanation:

Let’s break it down:

- The set {12, 28, 32}:

- 12 = 2 × 2 × 3

- 28 = 2 × 2 × 7

- 32 = 2 × 2 × 2 × 2 × 2

- Notice, all numbers have 2 as the only repeating prime factor. They are all even numbers, heavily based on the prime 2.

Now let’s look at the options:

1. {39, 78, 102}

- 39 = 3 × 13

- 78 = 2 × 3 × 13

- 102 = 2 × 3 × 17

- These are all divisible by 3, but odd numbers are mixed in, and they aren't strictly tied to powers of 2 or to even/odd patterns the same way.

2. {15, 35, 45}

- 15 = 3 × 5

- 35 = 5 × 7

- 45 = 3 × 3 × 5

- Odd numbers, mainly divisible by 5 or 3. Again, no strong 2/prime pattern.

3. {9, 21, 24}

- 9 = 3 × 3

- 21 = 3 × 7

- 24 = 2 × 2 × 2 × 3

- Only 24 is even and has 2 as a factor; the rest are odd. This does not match the original set's idea of all numbers tied to powers of 2.

4. {21, 48, 56}

- 21 = 3 × 7 (odd)

- 48 = 2 × 2 × 2 × 2 × 3

- 56 = 2 × 2 × 2 × 7

- The even numbers, 48 and 56, are heavy on the 2’s just like the original set, and both are even, but 21 is odd and breaks the pattern.

What this really means is: None of the new sets perfectly copy the exact structure of having only even numbers with powers of 2, but option 4: {21, 48, 56} comes closest—two numbers with lots of 2s as factors, mirroring the spirit of {12, 28, 32}.

Option 4 is the correct answer.