First off lets calculate the moles in the original solution.
What is the molar mass of sodium chloride? Na=23.0 and Cl=35.5 (I am choosing 3 sf as that is the periodic table I have on hand but 23.512g is 5SF) MM=58.5 (3SF but you should do 5SF)
Mass/Molar mass = moles 23.512g/58.5gmol-1=0.402 moles (3SF)
Mol X Vol=moles. Lets check what we have. We know the moles and we know the volume 250.00 mL therefore rearranging our equation Mol=moles/vol (note molarity is moles per liter so for dimensional analysis volume needs to be 0.250L)
0.402 moles/0.250L=1.61M (3SF remember you could be doing this to 5)
Now we are going to take 10mL of our 1.61 M solution.
We will use the equation
Mol X Vol = moles for our final answer
Vol needs to be in litres so we will divide 10 by 1000 to get 0.01L (note 10.0mL was 3 SF so now our answer really should be 3SF)
1.61 M (moles/L) X 0.01L = 0.0161 moles
Hope this all makes sense.