The function $g$ is defined as $g(x)=\frac{7}{2 x^{2}-4 x}$. Find $g(x+6)$ Write your answer without parentheses, and simplify it as much as possible.

Step 1 ：Let's find the function $g(x+6)$ by substituting $x+6$ into the function $g(x)$.

Step 2 ：Substitute $x+6$ into the function $g(x)$: $g(x+6) = \frac{7}{2(x+6)^{2}-4(x+6)}$

Step 3 ：Simplify the denominator: $g(x+6) = \frac{7}{2(x^{2} + 12x + 36) - 4x - 24}$

Step 4 ：Further simplify the denominator: $g(x+6) = \frac{7}{2x^{2} + 24x + 72 - 4x - 24}$

Step 5 ：Combine like terms in the denominator: $g(x+6) = \frac{7}{2x^{2} + 20x + 48}$

Step 6 ：\(\boxed{g(x+6) = \frac{7}{2(x^{2} + 10x + 24)}}\)