Why is there a deadweight loss in this lemons market?
You can calculate the total social surplus (= CS + PS) in this equilibrium and compare it to the social surplus in the efficient allocation of cars. 

Equilibrium allocation

The equilibrium (under asymmetric information) has price equal to $12000$. Thus, in the lemon's market,
\begin{align}
CS_L&amp;=(8000-12000)\times1000=-4000000\\
PS_L&amp;=\frac12\times(12000-2000)\times1000=5000000.
\end{align}
Total social surplus in the lemon's market is 
\begin{equation}
TS_L=CS_L+PS_L=1000000.
\end{equation}
In the plum's market, 
\begin{align}
CS_P&amp;=(16000-12000)\times400=1600000\\
PS_P&amp;=\frac12\times(12000-4000)\times400=1600000.
\end{align}
Total social surplus in the lemon's market is 
\begin{equation}
TS_P=CS_P+PS_P=3200000.
\end{equation}
Joint surplus from the two markets: 
\begin{equation}
TS=TS_L+TS_P=4200000.
\end{equation}

Efficient allocation

Efficiency occurs when lemons are priced at $8000$ and plums at $16000$. Note that in both markets, since demand is perfectly elastic, consumer surplus is zero at the efficient allocation. So total surplus is the same as producer surplus. 
\begin{align}
TS_L^*&amp;=\frac12\times(8000-2000)\times600=1800000\\
TS_P^*&amp;=\frac12\times(16000-4000)\times600=3600000\\
TS^*&amp;=TS_L^*+TS_P^*=5400000.
\end{align}



The gap between $TS^*$ and $TS$ is the DWL. The inefficiency arises from the fact that, in equilibrium (with asymm info), some cars are in the wrong hands: the last 400 lemons sold and the potential 200 plums that were unsold.