Find the 12th term of the geometric sequence shown below. \[ 6 x^{8},-12 x^{12}, 24 x^{16}, \ldots \]

Step 1 ：The given sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. In this case, the ratio is \(-2x^4\).

Step 2 ：The nth term of a geometric sequence can be found using the formula: \(a * r^{(n-1)}\) where: \(a\) is the first term of the sequence, \(r\) is the common ratio, and \(n\) is the term number.

Step 3 ：So, to find the 12th term, we can substitute \(a = 6x^8\), \(r = -2x^4\), and \(n = 12\) into the formula.

Step 4 ：By substituting these values into the formula, we get the 12th term as \(-12288x^{52}\).

Step 5 ：Final Answer: The 12th term of the geometric sequence is \(\boxed{-12288x^{52}}\).