12 n - 2 t = - 2 w The given equation relates the variables n

Choice D is correct. Adding $\frac{2}{t}$ to each side of the given equation yields $\frac{12}{n}=-\frac{2}{w}+\frac{2}{t}$. The fractions on the right side of this equation have a common denominator of $tw$; therefore, the equation can be written as $\frac{12}{n}=\frac{2w}{tw}-\frac{2t}{tw}$, or $\frac{12}{n}=\frac{2w-2t}{tw}$, which is equivalent to $\frac{12}{n}=\frac{2\left(w-t\right)}{tw}$. Dividing each side of this equation by $2$ yields $\frac{6}{n}=\frac{w-t}{tw}$. Since $n$, $t$, $w$, and $w-t$ are all positive quantities, taking the reciprocal of each side of the equation $\frac{6}{n}=\frac{w-t}{tw}$ yields an equivalent equation: $\frac{n}{6}=\frac{tw}{w-t}$. Multiplying each side of this equation by $6$ yields $n=\frac{6tw}{w-t}$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is equivalent to $\frac{1}{n}$ rather than $n$.