So to approach this problem, we have to express mM as milimolar, which is just the -mili prefix added to molarity, which is expressed as moles/liter.
Let's take part A as an example,
200mM sucrose= 200 x10^-3 moles/L
The problem says 100mL of solution are used instead of a typical Liter used for units of molarity.
So now, we can set up an equation. Some number of moles divided by 100mL (or .1L)= 200mM (or 200*10^-3 moles/L)
x/.1L= 200*10^-3 moles/L
Solving for x, we get that x= .02 moles
Once we obtain the number of moles necessary, all we have to do to find the amount of sugar needed is multiplying the number of moles by the molar mass, in this case Part A asks about sucrose.
(.02 moles)(342grams/mole sucrose)= 6.84 grams of sucrose needed to make a 200mM sucrose solution with 100mL of solution.
For the following parts, you can follow this method and obtain the correct answer every time! Hope this helps.