Answer
$Q_L=3.646\times10^{12}\ kWh$
Work Step by Step
Since
$\eta = W_e/Q_H$
$Q_H=W_e+Q_L$
which leads to
$\eta(W_e+Q_L) = W_e$
Given $\eta=0.34,\ W_e=1.878\times10^{12}\ kWh$:
and solving for the heat loss:
$Q_L=3.646\times10^{12}\ kWh$