I think "properly nested" graphs represent any one of the below:
- inner loops of begin-end which is enclosed in the outer loop of parbegin-parend
- inner loops of parbegin-parend which is enclosed in the outer loop of begin-end. (Example of this is the below diagram.)
And the question is asking for precedence graph of processes that can be implemented using only parbegin and parend. I think it is different from "properly nested" graphs. The graph expected in the question would be as the below diagram. (I don't know the exact name given for these type of precedence graphs)
Reference: https://www.ics.uci.edu/~bic/os/OS/PROOFS/bicc02v2.pdf
An important class of process flow graphs are those that are properly nested. Let S(p1,...,pn) denote the serial execution of processes p1 through pn and let P(p1,...,pn) denote the parallel execution of processes p1 through pn. Then a process flow graph is properly nested if it can be described by the functions S and P, and only function composition.