Calculating Variance of Y in linear regression model given variance of X and e where e = error term I'm confused about the calculation in the below problem. We're given Var(X) and Var(e) but where does the 2^2 term come from (or is that a Z^2?)? What formula for calculating variance is being used here?

 A: The $2^2$ (it's definitely a $2$, not a $z$) arises from a basic property of variances:
$$\text{Var}(kX)=k^2\text{Var}(X)\,.$$
http://en.wikipedia.org/wiki/Variance#Basic_properties
So $\text{Var}[(-2)X]=(-2)^2\text{Var}(X)=2^2\text{Var}(X)$
The remaining part uses another of the basic properties (see the above link again) - that the variance of the sum of independent variables is the sum of the variances 
$$\text{Var}(X_1+X_2)=\text{Var}(X_1)+\text{Var}(X_2)\,,$$ 
for $X_1,X_2$ independent - or in short, when you have independence, 'variances add'. 
Note that the independence of $X$ and $\epsilon$ is not explicitly stated there, but in ordinary linear regression, they are assumed independent.
Putting it all together:
$\text{Var}(Y) = \text{Var}(10-2X+\epsilon)$
$\quad\quad\quad\,\,\,=\text{Var}(-2X+\epsilon)\quad\quad\quad\quad\quad\,\;$     $_{(Var(c+X)=Var(X))}$
$\quad\quad\quad\,\,\,=\text{Var}(-2X)+\text{Var}(\epsilon)\quad\quad\quad\,$     $_\text{(independence)}$
$\quad\quad\quad\,\,\,=(-2)^2\text{Var}(X)+\text{Var}(\epsilon)\quad\quad$     $_{(Var(kX)=k^2Var(X))}$
$\quad\quad\quad\,\,\,=4\text{Var}(X)+\text{Var}(\epsilon)\quad\quad\quad\quad$     $_\text{(elementary arithmetic)}$
