Explanation:

Let’s break it down:

- The pattern links the first number to the second: 396 to 24.

- What stands out? 396 ÷ 24 = 16.5. Not an integer.

- Try something else: 3 + 9 + 6 = 18. 396 ÷ 18 = 22. Not the pair.

- How about factors? 396/24 = 16.5, so maybe it's *not* division.

- Instead, count the number of divisors. 396 has 18 divisors. Not 24.

- Let's factor 396:

- 396 = 2 × 2 × 3 × 3 × 11

- 24 = 2 × 2 × 2 × 3

Actually, let's look at the 672:30 side.

- 672 : 30

- 6 + 7 + 2 = 15

- 672/30 = 22.4

- Let’s try adding digits of the first number and multiplying by something. 396’s digits sum to 18. 18 × 1.33 is about 24, but that's rough.

- Now, factor 396. What’s half of 396? 198. 396/24=16.5.

- 24 is a factor of 396, so maybe all these second numbers are factors of the first.

OK, new trick: What if we factor the second number and multiply it by something? Still not a clear pattern.

Let’s just use option plugging:

- Use pattern matching for unknown x: x : 28.

- The third pair: 672 : 30. 672/30=22.4.

Check options:

- 1) 504/28 = 18

- 2) 572/28 = 20.428

- 3) 588/28 = 21

- 4) 536/28 = 19.14

Look at the differences:

- 396/24 = 16.5

- So the 672 pair is 22.4, not matching.

Wait. Maybe it's the sum of the digits of both numbers:

- 396 + 24 = 420

- 28 + x = ?

- 672 + 30 = 702

No pattern.

What about 396, 504, 572, 588, 536, 672? Are they in arithmetic progression? No.

BUT: Try their ratio sequence: 24/396, 28/x, 30/672.

- 24/396 = 0.0606

- 28/…? Let's try all options:

- 28/504=0.0556

- 28/572=0.0489

- 28/588=0.0476

- 28/536=0.0522

- 30/672=0.0446

See the third pair, 28/588 and 30/672 are very close in ratio.

- 28/588 ˜ 0.0476

- 30/672 ˜ 0.0446 ; difference is roughly the same as going from 0.0606 to 0.0476.

- 24/396 > 28/588 > 30/672 : pattern—decreasing ratio.

So, the answer with the closest matching ratio is option 3, 588.

Correct answer: Option 3, 588

Here's what really matters: the sequence uses a decreasing ratio pattern, and 588 fits it best.