Choose the next term of the series 6, 18, 108, 1296, _______.

The correct option is 31104.

To find the next term of the series, let us analyze the relationship between consecutive terms in the given sequence: 6, 18, 108, 1296, ______.

We can determine the factor by which each term is multiplied to get the subsequent term:
- From the 1st term to the 2nd term: $$6\times 3=18$$ - From the 2nd term to the 3rd term: $$18\times 6=108$$ - From the 3rd term to the 4th term: $$108\times 12=1296$$

Let us look at the sequence of multipliers: 3, 6, 12, ...
We can observe that each multiplier is obtained by doubling the previous one:
$$3\times 2=6$$
$$6\times 2=12$$

Following this pattern, the next multiplier in the sequence must be:
$$12\times 2=24$$

Therefore, to find the next term of the series, we multiply the 4th term (1296) by this next multiplier (24):
$$1296\times 24=31104$$