Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.

5 : 45 :: 3 : 3 :: 6 : ?

The correct answer is 96.

To find the pattern, we must analyze each given pair and discover the relationship between the first number and the second number.

Step 1: Analyze the first pair — 5 : 45

We need to find what operation on 5 gives 45.

Notice that: $5-2=3$, and $3{}^2=9$

So: $5\times {(5-2)}^2=5\times 3^2=5\times 9=45$ ✓

Step 2: Verify with the second pair — 3 : 3

Apply the same formula:

$3\times {(3-2)}^2=3\times 1^2=3\times 1=3$ ✓

The pattern is confirmed: second number = first number × (first number - 2)²

Step 3: Apply the formula to the third pair — 6 : ?

$6\times {(6-2)}^2=6\times 4^2=6\times 16=96$

Summary of the pattern:

5 : 45 → $5\times 3^2=45$
3 : 3 → $3\times 1^2=3$
6 : ? → $6\times 4^2=96$

The missing number is 96.