Conceptual understanding of solution / solute in a question 6.853g of sodium cyanide was dissolved in water and brought to volume in a 100ml volumetric flask. The final mass of the solution was found to be 107.166g 

My understanding -

A solution is understood when I put a solute into a solvent (water) and dissolves it. 

So in this case, if I wanted to find the composition of solution expressed as moles, 
I must take mass multiply by the molecular weight of Sodium Cyanide, do I use the mass of the solution or the mass of solute ? 

With this then I can go on to find molarity, normality as well as weight percent (mass of solute/mass of total solution) and weight/volume percent (mass of solute/volume of total solution).
Mole fraction is the ratio of the number of mole of a component to that of the number of moles of the total mixture. In your case, 6.853g of NaCN equals 6.853/49.002 = 0.139 moles.

The rest is water i.e. 107.166 - 6.853 = 100.313g. this corresponds to (100.313/18.015) = 5.568 moles.

Now, total moles = 0.1398 + 5.568 = 5.708moles.

The mole fraction of NaCN = 0.139/5.708 = 0.024.