Hi Jas A.!
The question hints to us that we should consider the loading dye dilution. We are told the stock is a 6X preparation. Because we want to run the dye at a 1X concentration, we must dilute it. What we must do is figure how much, or what volume, of the stock we need for our 10μL sample volume. For this, we can use the dilution equation:
M1V1 = M2V2 => V1 = M2V2/M1
V1 represents the volume of our stock concentration that we will need.
V1 = M2V2/M1
<=> (1X*10μL)/6X
V1 = 1.7μL of loading dye
Please note that we can use any units for both the concentration and volume variables. We need not adhere to simply using molarity and liters, so long as we are consistent in our problem. For instance, you must use mL for V2 if you also used mL for V1. You cannot use mL for V2 if you used μL for V1.
To find the volume of water for the proper dilution, we simply subtract:
Vsample + Vdye + VH2O = Vtotal => VH2O = Vtotal - (Vsample + Vdye)
<=> 10μL - (1μL + 1.7μL)
VH2O = 7.3μL
It is noteworthy that running multiples of 6μL would be ideal with such a stock concentration.
Hope this helps!
Cheers