The given series is 4, 6, 8, 30, 112, ? and we need to find the missing term.

To determine the pattern in the series, let's calculate the differences between each consecutive term:

6 - 4 = 2
8 - 6 = 2
30 - 8 = 22
112 - 30 = 82

The differences are not constant, so it's not an arithmetic progression. Let's try calculating the ratios between each consecutive term:

6 / 4 = 1.5
8 / 6 = 1.33
30 / 8 = 3.75
112 / 30 = 3.73

The ratios are not constant either, so it's not a geometric progression.

From the given information, we can observe that the differences and ratios are not consistent, which suggests that there might be a different pattern at play.

Upon closer inspection, we can see that each term in the series is obtained by multiplying the previous term by a number and then adding a constant:

4 * 1.5 + 2 = 8
8 * 3.75 + 22 = 30
30 * 3.73 + 82 = 112

To find the missing term, we need to apply the same pattern to the last term:

112 * 3.73 + 82 = 570

Therefore, the missing term in the series is 570.

Hence, the correct answer is option E) 570.