This is from Stanley's Catalan Numbers, problem 36:
I have difficulty understanding the problem: there is no $L$, $L$'s endpoints lie on $P$ (what is $P$?) and every point of $L$ lies on or below $D$, right? Equivalently, for every such segment $L$, the endpoints are not both on $P$, or some point of $L$ lies above $D$. If we look at the 4th path and take $(i,j)=(2,2)$, then the endpoints are on the path and the segment is above the path? The line $y=2$ is like a tunnel underneath which the path goes. Do I have to read his Enumerative Combinatorics before reading this? There are quite a few terms that I cannot understand. Thanks in advance.