Preferences over lotteries
A lottery is essentially a probability distribution. So the variance of a lottery is the variance of the probability distribution it represents, which is given by the formula 
\begin{equation}
\mathrm{Var}(L)=\sum_{i=1}^np_i(x_i-\mathbb E(L))^2,
\end{equation}
where $p_i$ is the probability that outcome $i$ occurs, $x_i$ is the monetary value of outcome $i$, and $\mathbb E(L)$ is the expected value of the lottery. 

Take the lottery $L_2=0.5[0]\oplus0.5[4]$ for example. We can easily verify that $\mathbb E(L_2)=2$. By the formula above, then, 
\begin{equation}
\mathrm{Var}(L_2)=0.5(0-2)^2+0.5(4-2)^2=4.
\end{equation}

I'll leave you to finish the rest of the question.