The answer is $\boxed{7434}$.
The series is $2, 6, 18, 54, 162, 486, 1458, 4374, \dots$. It is a geometric series with a first term of $2$ and a common ratio of $3$. The general formula for a geometric series is $a_n = a_1 r^{n-1}$, where $a_n$ is the $n$th term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. In this case, we have $a_1 = 2$ and $r = 3$. To find the eighth term, we can substitute $n = 8$ into the formula:
$$a_8 = 2 \cdot 3^{8-1} = 2 \cdot 3^7 = 2 \cdot 2187 = \boxed{7434}$$
Option A is incorrect because it is the sum of the first eight terms of the series, which is $2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 = 2420$.
Option B is incorrect because it is the sum of the first seven terms of the series, which is $2 + 6 + 18 + 54 + 162 + 486 = 870$.
Option C is incorrect because it is the sum of the first six terms of the series, which is $2 + 6 + 18 + 54 + 162 = 292$.