Here is another way to do it:
Separate the variable (n) from the rest of the equation.
\(\displaystyle \frac{{10}}{8} = \frac{6}{n} + 2 \\\)
Since 2 is added on the right, you must do the oposite to the left (subtract).
\(\displaystyle \frac{{10}}{8} - 2 = \frac{6}{n} \\
- .75 = 6*\frac{1}{n} \\\)
Since 6 is multiplied on the right, you must do the oposite to the left (divide).
\(\displaystyle - \frac{{.75}}{6} = \frac{1}{n} \\
- \frac{1}{8} = \frac{1}{n} \\
n = - 8 \\\)