If two people collaborate on a work: the (3,3) means if neither of them do any work, then, they have to be put on detention for 1 hour and then both of them still have to finish the same 2-hour work without any help. (1,1) means if both of them work together, each of them spends 1 hour.
I think the Nash Equilibrium is only (1,1), because (3,3) is worse than all other choice and of course each of them knows the other will not choose (2,0) or (0,2)
Is it correct?
The game $$\begin{array}{|c|c|c|} \hline P1\backslash P2 & \text{ together T } & \text{ let the other L} \\ \hline \text{together T} & -1,-1 & -2,0 \\ \hline \text{let the other L} & 0,-2 & -3,-3\\ \hline\end{array}$$
has two Nash eq: (T,L) and (L,T).
(T,T) and (L,L) are not Nash.
The way to prove some action profile is a Nash equilibrium is to look at best responses. At a Nash equilibrium, no one wants to change his action if he thinks the other will not change.
Nash equilibrium outcomes can be very bad (or very good), there is not point in trying to decide whether an outcome is Nash simply because it is bad or good. The idea is that if the other is playing Nash then you can not do better by playing something that is not Nash.