Find the number that should fill the position of the question mark (?) in the following sequence.

4, 262, 460, 606, 708, ?

The correct option is 774.

To find the missing number in the given sequence, let us analyze the differences between consecutive terms:

First term = 4

Second term = 262

Difference = $262-4=258$

Third term = 460

Difference = $460-262=198$

Fourth term = 606

Difference = $606-460=146$

Fifth term = 708

Difference = $708-606=102$

Now, let us examine the sequence of first-level differences: 258, 198, 146, 102.

Let us find the differences between these consecutive difference terms (second-level differences):

$258-198=60$

$198-146=52$

$146-102=44$

Notice that the second-level difference decreases by 8 each time ($60-8=52$, and $52-8=44$).

Following this pattern, the next second-level difference should be:

$44-8=36$

Therefore, the next first-level difference is calculated as:

$102-36=66$

Finally, we add this difference to the fifth term to get the missing term (?):

$708+66=774$

Thus, the number that fills the position of the question mark is 774.