I don't think you've read the question correctly, you should be proving that:
$$ Var[Di - \mu Vi] = E[Di] $$
To go about that you use the fact that:
$$ Var[Di - \mu Vi] = E[(Di- \mu Vi)^2] - (E[Di- \mu Vi])^2 $$
Where the second term is naturally 0 as you've proved in statement (4.2)
The first term is what you attain from splitting up the pdf into the two values that Di takes on: 0 or 1, and then making the substitution from taking the derivative of the expression given twice.