Explanation:

Let’s break it down:

- We’re given this pattern: 3 : 17 :: 6 : ? :: 9 : 47

- Our job is to figure out what links each pair, then fill in the blank.

So, let's see the pattern:

- 3 : 17. What’s happening?

3 × 3 = 9, 9 + 8 = 17.

- 9 : 47. Test if the same rule works:

9 × 3 = 27, 27 + 20 = 47.

But the added number (8, then 20) is not consistent.

- Let's try another way:

3 ? 17 (if we try n × n + n, 3 × 3 + 3 = 12), nope.

What about n × 5 + 2? 3×5=15, 15+2=17. Works for 3.

Test for 9: 9×5=45+2=47. Aha! That's the pattern!

- So, the rule: Each number ? (number × 5) + 2

Now, apply this to 6:

- 6 × 5 = 30, 30 + 2 = 32

Let’s see which option says 32:

Option: 1, 34

Option: 2, 36

Option: 3, 38

Option: 4, 32

So, the correct answer:

Option: 4 – 32.