Calculating the concentration of a diluted solution
The answer is basically correct (see note at the end of my answer about significant figures) but there is a simpler method, using a dilution factor.  

The original volume of your solution was 2 mL, and the final volume was 12 mL, so the dilution factor is simply $\frac{2}{12}$.  

The original concentration times the dilution factor gives the final concentration:  

$$\pu{10\frac{mg}{L}}\cdot\frac{2}{12} = \pu{1.7\frac{mg}{L}}$$  

Note that only 2 significant figures were given in the problem and your answer reported 3.