Explanation:

Let’s break it down step by step:

- 8 : 24

- 8 × 3 = 24

- ? : 52

- We need to find a number which, using the same logic, gives 52.

- 18 : 114

- 18 × 6 + 6 = 114

None of the patterns (simple multiplication, addition, etc.) are sticking at first glance. Let's test common options:

Option 1: 12

- 12 × ? = 52 ? 52 ÷ 12 ˜ 4.33 (not a whole number)

Option 2: 14

- 52 ÷ 14 ˜ 3.714 (again, doesn’t match the nice multiplication)

Option 3: 20

- 52 ÷ 20 = 2.6 (no)

Option 4: 16

- 16 × 3.25 = 52

Let’s try adding something:

- 8 × 3 = 24

- 18 × 6 + 6 = 114 (not just ‘times’ something)

- 18 × 6 + 6 = 18 × (6 + ?) = 114

But 8 × (3 + ?) = not 24, 8 × 3 = 24 exactly.

Maybe the difference between products is consistent:

- 8 × 3 = 24

- 16 × 3.25 = 52

- 18 × 6 + 6 = 114

But 16 × 3.25 isn’t a usual pattern.

It seems the intended pattern is:

- 8 × 3 = 24

- 18 × 6 + 6 = 114

So between 8 and 18, the multiplier doubles (3 to 6), and you add the multiplier also.

Let’s see if it works backward:

- 24 × 2 = 48 ? that's not the first pair.

Compare the sequences directly:

- 8 to 24 (×3)

- ? to 52

- 18 to 114 (×6 + 6)

But none of the options, when multiplied by a whole number, give 52.

Try 14:

- 14 × 3 + 10 = 52

But this doesn’t work somewhere else.

Try 16:

- 16 × 3 = 48 (close to 52)

- 16 × 3.25 = 52

So, technically, none of the options fit the pattern super cleanly, but 16 × 3.25 = 52 at least works mathematically.

Based on these checks, the pattern isn’t super clean, but out of those, Option 4, 16 makes the math work.

So, Option 4: 16 is the answer.

Here’s the thing:

- 12, 14, and 20 don’t give a whole number multiplier or clear pattern.

- 16 × 3.25 = 52, actually produces 52.

- While the logic isn’t perfect, that’s the only option that returns 52 with multiplication.

So, Option 4: 16 it is.